As the Biden camp secured victories in Michigan and Wisconsin critical to its path to victory, attention shifted on Thursday to a handful of states where the result remained too close to call and to the courts, where the Trump campaign filed a barrage of lawsuits challenging the validity of the count.
In Arizona, where ballots continued to be tallied even as roughly 150 Trump supporters, some armed, surrounded a facility in Maricopa County to voice support for President Trump as he continued to chip away at former Vice President Joseph R. Biden’s lead in the state.
After 62,000 votes in Maricopa County were added to the tally early Thursday, Mr. Biden led Mr. Trump in Arizona by 68,400 votes, or less than three percentage points. But Mr. Trump faced a steep uphill battle to close the gap.
But the tense scenes outside the Arizona vote counting station reflected a deeper sense of unease rippling across the nation.
After a campaign that exposed the deep rifts in a nation more polarized than at any time in modern memory, each announcement of new vote totals stoked varying degrees of relief, outrage and anxiety from the competing factions.
Mr. Biden, projecting confidence but stopping short of declaring victory as Mr. Trump did on election night, sought to strike a conciliatory note when he spoke to supporters on Wednesday afternoon.
But he also had a warning for the Trump team.
“Power can’t be taken or asserted,” he said. “It flows from the people. And it’s their will that determines who will be the president of the United States, and their will alone.”
If Biden supporters’ hearts jumped with each new total in Arizona that cut into the former vice president’s lead, they were buoyed by new tallies in Georgia, where Mr. Trump’s lead narrowed to only 23,039 votes — with nearly all of the counties with appreciable outstanding votes tinted blue on the map.
And while Mr. Biden has several routes that would allow him to secure the necessary 270 electoral votes, Mr. Trump also needs to win Pennsylvania.
That battleground state, with the largest trove of electoral votes still up for grabs, had more than one million outstanding mail-in ballots to count as Mr. Trump’s lead narrowed to fewer than 200,000 votes early Thursday.
As Mr. Trump’s political path grew more precarious, his team turned to the courts, filing lawsuits and demanding a recount in Wisconsin.
The Trump campaign’s bid to stave off defeat stretched from the Supreme Court, where the campaign intervened in a case challenging Pennsylvania’s plan to count ballots received for up to three days after Election Day, to individual counties where the campaign showed a willingness to fight over even the smallest batch of votes.
The political tensions started to spill into the streets, protesters staging demonstrations in Minneapolis, Seattle, Phoenix, Philadelphia, New York City and Portland, Ore.
While mostly peaceful, with chants demanding that every vote be counted, in Portland store windows were shattered as some protesters grappled with the police. In Minneapolis, demonstrators shut down a freeway and dozens were arrested.
At least 58 people were arrested in connection with demonstrations in New York after a day of peaceful marches turned into a chaotic night of clashes.
At the same time, supporters of Mr. Trump descended on vote-counting facilities in several contested states.
They had a different demand.
“Stop the count,” they yelled outside a facility in Detroit.
But inside, the democratic process continued to play out as election workers — socially distanced and wearing masks — went about their job: counting the votes.
Here is the state of play in battleground states as of 3 a.m. Eastern on Thursday.
Electoral votes: 11
Biden leads Trump, 50.5 percent to 48.1 percent, with 86 percent of the estimated vote in.
To keep in mind: Trump needs to win nearly two-thirds of the remaining votes to capture the state. Officials in Maricopa County, the state’s most populous county and home to Phoenix, said they would release the next results update Thursday night.
Electoral votes: 16
Trump leads Biden, 49.6 percent to 49.1 percent, with 95 percent of the estimated vote in.
Keep in mind: Many of the votes still coming in are in suburbs of Atlanta and other populous counties that have been breaking for Biden. Mr. Biden must win around 60 percent of the remaining votes to pull ahead. Georgia’s secretary of state said that he was expecting workers to continue tallying votes until late Wednesday or Thursday.
Electoral votes: 6
Biden leads Trump, 49.3 percent to 48.7 percent, with 86 percent of the estimated vote in.
Keep in mind: Mr. Biden leads by fewer than 8,000 votes, but all of the Election Day vote has been counted, leaving only Democratic-leaning late mail and provisional ballots to be tabulated. Officials said results would be released around noon Eastern on Thursday.
Electoral votes: 15
Trump leads Biden, 50.1 percent to 48.7 percent, with 95 percent of the estimated vote in.
Keep in mind: With most votes now tabulated, Biden would need to win about two-thirds of the remainder to pull ahead. Mail ballots postmarked by Election Day will be accepted until Thursday, Nov. 12.
Electoral votes: 20
Trump leads Biden, 50.7 percent to 48.1 percent, with 89 percent of the estimated vote in.
Keep in mind: Most of the votes yet to be counted are in counties where Biden is ahead, including Philadelphia, the state’s most populous county, where Biden leads by about 60 percentage points, and Allegheny, which Biden leads by over 10 points and which includes Pittsburgh. But plenty of votes are outstanding in dozens of smaller Trump-leaning counties.
Biden needs to win about two-thirds of the remaining votes to win the state. Officials have said they expect most votes to be counted by Friday.
Electoral votes: 16
Biden was declared the winner on Wednesday. The vote now stands at 50.4 percent to 48 percent, with more than 98 percent of votes counted.
Keep in mind: Before the Michigan race was called, the Trump campaign had announced that it was suing to halt the counting of mail-in ballots there because of what it called insufficient transparency in the process.
Electoral votes: 10
Biden was declared the winner, 49.4 percent to 48.8 percent, a margin of 0.6 percentage points, with more than 98 percent of votes counted.
Keep in mind: Wisconsin law allows a recount when the leading candidate’s margin is less than one percent, and the Trump campaign said it would request one.
ATLANTA — The presidential race in Georgia appeared headed for a photo finish as former Vice President Joseph R. Biden Jr. steadily gained ground on President Trump. The victor will be awarded 16 electoral votes.
Mr. Biden began Wednesday morning approximately 100,000 votes behind Mr. Trump, but as county elections workers around the state continued the laborious tabulation of absentee ballots into Thursday morning, Mr. Trump’s lead narrowed to 23,000 votes, or 0.5 percent. Under Georgia election law, a candidate may request a recount if the margin is 0.5 or less.
In Fulton County, a Democratic stronghold and home to most of Atlanta, Mr. Biden narrowed the margin by more than 18,000 votes between 5 p.m. and midnight as the work of processing and tabulating the votes continued. In DeKalb County, also part of the metropolitan region, Mr. Biden narrowed it by an additional 5,000. The next update from Georgia’s secretary of state is scheduled for 10:30 a.m. Thursday.
Brad Raffensperger, the Georgia secretary of state, said that as of 10:15 p.m. Wednesday, about 90,735 ballots still needed to be counted. More than a third of them were in Fulton and DeKalb counties.
If the trajectory of Mr. Biden’s gains continued, it appeared he could overtake Mr. Trump in Georgia by the final tally on Thursday. The question was whether additional absentee votes from rural and more Republican areas would offset enough of Mr. Biden’s gains to preserve Mr. Trump’s lead.
Republicans in Georgia were nervously assessing the vote count and promised to file lawsuits in a dozen or more counties aimed at knocking off votes here and there. The first case, filed in Savannah on Wednesday, was an effort to chisel away 53 ballots that Georgia Republicans said had arrived too late to be counted.
Calling on election officials to “count every vote,” protesters marched through the streets of several American cities on Wednesday in response to President Trump’s aggressive effort to challenge the vote count in Tuesday’s presidential election.
A crowd of more than 150 supporters of President Trump gathered Wednesday night in front of the Maricopa County Recorder’s building near downtown Phoenix to protest what they described as efforts to cast President Trump as losing Arizona.
Many in the crowd were holding Trump flags, and numerous people were wielding AR-15 rifles and other firearms. Some in the crowd chanted “Down With Fox,” a criticism of the television network’s decision to call Arizona for Mr. Biden.
“The only way Biden can win Arizona is through fraud,” said Jim Williams, 67, a welder who attended the protest. “I won’t accept a Biden victory. I don’t want to live under Communist rule.”
At several points, protesters contended that Adrian Fontes, the county official who oversees elections in Maricopa County, was improperly failing to count some ballots and costing Mr. Trump votes in Arizona’s most populous county — although there was no evidence that any ballots had been improperly tossed.
Keely Varvel, chief deputy for the Maricopa County Recorder, said there were no plans to halt counting of the ballots because of the protest in front of the building. ”We are still planning to finish up our scheduled ballot processing work and report out more results tonight,” Ms. Varvel said.
In Minneapolis, protesters blocked a freeway, prompting arrests. In Portland, hundreds gathered on the waterfront to protest the president’s attempted interventions in the vote count as a separate group protesting the police and urging racial justice surged through downtown, smashing shop windows and confronting police officers and National Guard troops.
Protesters also gathered in Philadelphia, Los Angeles, Chicago and elsewhere, some of them continuing the protests over racial justice and policing that have rocked the country since the police killing of George Floyd in Minneapolis in May. More demonstrations were scheduled for the coming days.
In Minneapolis, several hundred protesters angered over the president’s declarations marched onto Interstate 94, prompting the police to clear the roadway.
“Our focus is on not allowing Donald Trump to steal this election from the American people,” Nekima Levy Armstrong, a lawyer who was part of the protest, said in a phone interview from the freeway. She said that the protesters had halted traffic and that the police, some on horses, had begun to make arrests and were not allowing protesters to leave.
The Minnesota State Patrol said on Twitter that it was arresting protesters and that demonstrating on the freeway “is illegal and very dangerous for pedestrians and motorists.”
In New York, protesters held a peaceful demonstration in Manhattan earlier on Wednesday calling for every vote to be counted and for racial equality, but hostile clashes between protesters and the police developed later on when protesters briefly shut down traffic in the West Village, and officers pushed protesters to the sidewalks and arrested at least 20 people.
Former Vice President Joseph R. Biden Jr. has maintained a steady but slightly narrowing lead in Arizona vote tallies after Election Day, with Latino voters lining up behind the former vice president in a state that President Trump won by three and a half percentage points in 2016.
As of early Thursday, Mr. Biden led Mr. Trump in Arizona by 68,400 votes, or less than three percentage points. In the votes so far from Maricopa County, which includes Phoenix, Mr. Biden leads by five percentage points, with about 5 percent of the total vote still outstanding.
Even Mr. Biden’s narrow edge underscored a profound political shift in Arizona, a longtime Republican bastion that has lurched left in recent years, fueled by rapidly evolving demographics and a growing contingent of young Latino voters who favor liberal policies.
The count was delayed in the early hours of Thursday, as dozens of Trump supporters demonstrated outside the Maricopa County election office where the votes were being counted.
In one of the brightest spots for Democrats so far, the former astronaut Mark Kelly defeated the state’s Republican senator, Martha McSally, in a special election, making Mr. Kelly and Kyrsten Sinema the first pair of Democrats to represent Arizona in the Senate since the 1950s.
Republican lawyers and Trump campaign officials on Wednesday began a wide-ranging legal assault to challenge Democratic votes in key swing states, part of a long-telegraphed, post-Election Day campaign to claim victory over Joseph R. Biden Jr. with help from the courts.
By midday Wednesday, the Trump campaign had announced that it was suing to halt the counting of mail-in ballots in Michigan because of what it called insufficient transparency in the process.
“President Trump’s campaign has not been provided with meaningful access to numerous counting locations to observe the opening of ballots and the counting process, as guaranteed by Michigan law,” said Bill Stepien, President Trump’s campaign manager.
Separately, the Trump campaign said it would seek a recount of the vote in Wisconsin, even before the race was called. Mr. Biden was named the winner there on Wednesday afternoon by The Associated Press, by a margin of more than 20,000 votes, or 0.6 percentage points.
In news briefings and interviews, campaign aides grounded their legal arguments in a claim that they were merely seeking to ensure that no votes get to count that should not count, rather than repeating the president’s own early-morning claims that all counting should have stopped on Election Day, when early and incomplete results showed him ahead in some battleground states that will help decide the Electoral College winner.
“If we count all legal ballots, the president wins,” Mr. Stepien said on a morning conference call with reporters.
Earlier in the morning, Mr. Trump had emerged from watching returns at the White House to say, “We’ll be going to the U.S. Supreme Court. We want all voting to stop,” a crude rendering of his campaign’s legal position that was legally meaningless and that drew bipartisan criticism.
Already on Wednesday the Trump and Biden campaigns were in Pennsylvania courts pressing dual lawsuits to invalidate provisional and corrected ballots by citizens who were informed before polls closed that problems with their mail-in votes had caused them to be rejected by election officials.
In Georgia, where the president clung to a slim lead by Wednesday evening, but where many votes still had not been counted in metro Atlanta, an area that favored Mr. Biden, the Trump campaign challenged the validity of 53 mail-in ballots in a lawsuit that was filed on Wednesday in a county court. About 46,000 votes separated the candidates in Georgia.
The Trump campaign claimed that poll workers in Chatham County, which includes Savannah, did not follow the proper chain of custody procedures to determine whether the ballots had been received by 7 p.m. on Election Day, and claimed that they mixed them in with ballots that had been validated.
The petition asks the court to issue an order that would force the local election board to “collect, secure and safely store” all absentee ballots it received after the deadline, and “provide an accounting” of the ballots, including the names of absentee voters and the times the ballots were received.
Trump campaign officials also indicated they were considering more legal action in Arizona and in Nevada, where the Trump campaign was already pressing a lawsuit protesting the counting process in the state’s largest county.
Biden campaign officials said they had readied contingencies and legal papers for any challenges the president and his allies might bring.
“We are prepared for any effort any Republicans make in any of these states,” said Bob Bauer, a senior adviser to Mr. Biden’s campaign. “As far as our own planning, we’re winning the election.”
The Biden campaign’s position marked a key difference from the last time the nation was in a similarly contested setting, in Florida in 2000. In that case, Al Gore, the Democrat, was behind in the returns and was portrayed by Republicans as seeking to snatch victory away from George W. Bush — a position that kept Mr. Gore at a disadvantage throughout the legal fighting that followed.
While there have been countless election cases filed around the nation, it is not clear which of them might reach the Supreme Court in the coming days.
But one candidate is already on the docket, and on Wednesday that Trump campaign said that it was intervening in the case, from Pennsylvania, which challenges a ruling by the state’s highest court that extended the deadline for receiving mail ballots by three days.
Last month, the court refused to put the Pennsylvania case on a fast track, but three justices indicated that the court might return to it later if need be.
Should the vote in Pennsylvania have the potential to determine the outcome in the Electoral College and should those late-arriving ballots have the potential to swing the state — two big ifs — the U.S. Supreme Court might well intercede.
Late last month, the justices refused a plea from Republicans to fast-track a decision on whether the Pennsylvania Supreme Court had acted lawfully when it ordered a three-day extension for ballots clearly mailed on or before Election Day, and for ballots with missing or illegible postmarks “unless a preponderance of the evidence demonstrates that it was mailed after Election Day.”
The justices’ refusal came a little more than a week after the court deadlocked, 4 to 4, on an emergency application in the case on Oct. 19.
Justices Clarence Thomas, Samuel A. Alito Jr., Neil M. Gorsuch and Brett M. Kavanaugh said they would have granted a stay blocking the Pennsylvania Supreme Court’s decision. On the other side were Chief Justice John G. Roberts Jr. and the court’s three-member liberal wing: Justices Stephen G. Breyer, Sonia Sotomayor and Elena Kagan.
Justice Amy Coney Barrett, who joined the court on Oct. 27, did not take part in the decision not to fast-track the case.
Justice Alito, joined by Justices Thomas and Gorsuch, criticized his court’s treatment of the matter, which he said had “needlessly created conditions that could lead to serious postelection problems.”
“It would be highly desirable to issue a ruling on the constitutionality of the State Supreme Court’s decision before the election,” Justice Alito wrote. “That question has national importance, and there is a strong likelihood that the State Supreme Court decision violates the federal Constitution.”
But there was not enough time, he wrote. Still, Justice Alito left little doubt about where he stood on the question in the case.
Pennsylvania officials have instructed county election officials to segregate ballots arriving after 8 p.m. on Election Day through 5 p.m. on Friday. That would as a practical matter allow a ruling from the Supreme Court to determine whether they were ultimately counted.
As the results rolled in on Tuesday night, a feeing of déjà vu arrived along with them. Pre-election polls, it appeared, had been misleading once again.
While the nation awaits final results from Michigan, Pennsylvania and a few other states, it is already clear — no matter who ends up winning — that the industry failed to fully account for the missteps that led it to underestimate President Trump’s support four years ago.
The misses raise the question whether the polling industry, which has become a national fixation in an era of data journalism and statistical forecasting, can survive yet another crisis of confidence.
“I want to see all the results in,” Christopher Borick, the director of polling at Muhlenberg College in Pennsylvania, said in an interview. “I want to see where those deviations are from pre-election polls and final margins. But there’s ample evidence that there were major issues again. Just how deep they are, we’ll see.”
In some states where many polls had projected Mr. Trump losing narrowly — like Ohio, Iowa and Florida — he had already been declared the winner by early Wednesday. And in states that had seemed more than likely to go for Mr. Biden, like Michigan and Nevada, results were too close to call as the official tallies trickled in. (In one such state, Wisconsin, Mr. Biden was declared the winner on Wednesday afternoon, by 0.6 percentage points.)
Given the ballots that have been counted, it is now clear that there was an overestimation of Mr. Biden’s support across the board, particularly with white voters and with men. And while polling had presaged a swing away from Mr. Trump among white voters 65 and over, that never fully took shape.
Partly as a result, Mr. Biden underperformed his expectations not only in polyglot states like Florida but in heavily white, suburban areas such as Macomb County, Mich., where he had been widely expected to do well.
Dr. Borick pointed out that while state-level polls had widely misfired in 2016, the same thing had generally not occurred in the 2018 midterm elections. This led him to conclude that Mr. Trump was a complicating factor.
“In the end, like so many Trump-related things, there may be different rules,” he said. “I’m a quantifiable type of human being; I want to see evidence. And I only have two elections with Donald Trump in them — but both seem to be behaving in ways that others don’t behave.”
Not every pollster fared poorly. Ann Selzer, long considered one of the top pollsters in the country, released a poll with The Des Moines Register days before the election showing Mr. Trump opening up a seven-point lead in Iowa; that appears to be in line with the actual result thus far.
And inevitably, Robert Cahaly and his mysterious Trafalgar Group — which projected a bunch of close races in the battlegrounds — will get another look from curious commentators wondering why it has been so close to accurate, both in 2016 and this year.
The firm was among the only pollsters to show Mr. Trump’s strength in the Midwest and Pennsylvania four years ago, and while its polls this fall may end up being a little on the rosy-red side, it appears to have gotten the horse race in many states closer than other pollsters, by not giving short shrift to Mr. Trump’s strengths.