Since the day he was sworn into office, President Trump has pursued policies and practiced politics with a single-minded focus on bedrock Republicans, showing little interest in appealing to independent voters. That has made him one of the most powerful figures ever in his party, and rewarded him with strong conservative support in his re-election campaign.

But Mr. Trump’s focus on his base at the expense of swing voters, who have historically been a key target for presidential campaigns, is almost certainly not enough to win him a second term in the White House, as even some Republicans concede.

A national poll of registered voters by The Times and Siena College shows Mr. Trump drawing 36 percent of the vote, a far cry from the 46 percent he won in 2016. Perhaps even more troubling for Mr. Trump is that he has not assembled a broad coalition of voters, which is critical to winning battleground states. While Republicans support him overwhelmingly, he has the support of just 29 percent of independents and nonaffiliated voters — 18 points behind Joseph R. Biden Jr., his Democratic opponent. Mr. Trump narrowly won independents in 2016, according to exit polls.

Whether Mr. Trump can still expand his support at this point, especially in the battleground states that are crucial to his Electoral College calculus, is an enormous challenge that the president, to date, has shown little interest in meeting. Much of the nation has recoiled from Mr. Trump’s brash conduct and harsh language in office, and at the same time has moved to the left on health care, civil rights, same-sex marriage and other issues.

“He is losing, and if he doesn’t change course, both in terms of the substance of what he is discussing and the way that he approaches the American people, then he will lose,” Chris Christie, the former Republican governor of New Jersey and a former close adviser to Mr. Trump, said on Sunday on ABC’s “This Week.”

The coronavirus pandemic and the nationwide social unrest have all contributed to Mr. Trump’s diminished standing, including among swing voters — only 17 percent of independents strongly approve of Mr. Trump’s job performance, the poll shows.

“It’s not enough to win re-election,” Sara Fagen, who was the White House political director for President George W. Bush, said of tactics focused on turning out the base. “In this environment, it will be difficult to win an election without expanding the number of people who support you.”

Mr. Trump has told advisers and allies that he has to run as himself and that he has defied polling experts before, pointing to 2016. He won the presidency despite losing the popular vote, with narrow wins in three states — Michigan, Wisconsin and Pennsylvania — that gave him an Electoral College victory.

In that first race he sought to appeal primarily to Republican voters, but his defiant, outsider message, with its emphasis on trade and immigration, drew Americans alienated by Washington, hungry for a change after eight years of Democratic rule and put off by Hillary Clinton, his Democratic opponent.

But Mr. Trump is facing a decidedly different electoral landscape this time around. The Times/Siena poll found 9 percent of registered voters were undecided, and presumably fall into the category of persuadable voters. They, like much of the country, hold unfavorable views of Mr. Trump’s job performance, and particularly his response to the pandemic and to the demonstrations that followed the killing of George Floyd by the Minneapolis police.

“I’m not a huge Biden fan. I think he’s a career politician and a member of the donor class,” said John-Crichton McCutcheon, 50, from Miami Beach, who voted for Mr. Trump last time and responded to the Times/Siena poll of voters in battleground states. “But with Trump, things have gotten so bad, I’m going to have to go with Biden.”

Donna Saylor, 67, a Democrat and a nurse who lives in Pittston, Pa., voted for President Barack Obama in 2012 and for Mr. Trump in 2016. “Unfortunately,” she said of her support for Mr. Trump. She intends to vote for Mr. Biden in November.

“I’m definitely not happy with Trump,” she said in an interview earlier this month. “Every time he opens his mouth, it causes trouble. He’s not unifying this country as he should be; he’s dividing it.”

ImageMr. Trump has the support of just 29 percent of independents and nonaffiliated voters — 18 points behind Joseph R. Biden Jr., the presumptive Democratic nominee.
Mr. Trump has the support of just 29 percent of independents and nonaffiliated voters — 18 points behind Joseph R. Biden Jr., the presumptive Democratic nominee.Credit…Erin Schaff/The New York Times

Mr. Trump has governed and led with a focus on conservatives from the day he was inaugurated with a speech warning of “American carnage.”

He has followed the promise of his speech with policies that have rallied the right wing to his side: remaking the American judiciary and particularly the Supreme Court, rolling back environmental regulations, cutting taxes and moving the U.S. embassy in Israel to Jerusalem.

Even if he wanted to engage voters beyond his most loyal supporters, he may find he has little latitude to maneuver after defining himself so vividly in public life, particularly in these last months.

Mr. Trump and his advisers have disputed polls showing him struggling, and signaled that in the months ahead they would seek to strip away some of Mr. Biden’s support with attacks on, among other things, his age and mental acuity. That could also raise doubts about the former vice president among the remaining undecided voters.

And for all their concerns about Mr. Trump’s response to the pandemic and to the demonstrations, these swing voters approve his handling of the economy, suggesting an avenue to victory for Mr. Trump in the fall should economic conditions begin to rebound.

“If I had to vote based on the economy — right now — I’m sorry, but it would be Trump,” said Cheryl VanValkenburg, a factory worker who lives in Watertown, Wisc., a Republican suburb. She said she voted for Mr. Trump in 2016.

Christina Stoutenburg-Sanchez, 30, who lives in Smiths Creek, Mich., about an hour north of Detroit, said she was unhappy with both Mr. Trump and Mr. Biden. She said she was leaning toward voting for Mr. Biden. “But as much as I don’t like Trump, if he rallied and really pulled it together for our country, I could be persuaded,” she said.

Dan Hazelwood, a Republican strategist, said Mr. Trump had been hurt by his unsteady response to the coronavirus pandemic and to the nationwide demonstrations protesting police brutality and systemic racism. But he believes Mr. Trump could still assemble a bloc of voters who would support him over Mr. Biden.

“Right now, Trump’s coalition needs motivation,” he said. “The economy and the pandemic have sucked the enthusiasm away. At least 50 percent of America has deep and serious policy concerns with Biden and the Democrats. A ‘choice’ election between two policy directions is the motivation that Trump’s coalition needs, and it is why Biden is trying to be vanilla.”

Swing voters have been the subject of varying interest by presidential campaigns for nearly half a century. As the nation grew increasingly polarized, their numbers diminished, and some analysts began to suggest that the era of the swing voter had passed, particularly as Mr. Trump appeared to ignore them.

But his difficulties now leave little doubt that there are indeed still many voters up for grabs, and that the entire nation is not locked in red or blue corners. Mr. Trump won Wisconsin narrowly in 2016, but now trails Mr. Biden there by 11 points, according to the Times poll. Overall, analysts estimate swing voters make up between 10 and 15 of the electorate nationally.

“If you want to win, you have to get a significant percentage of the swing voters,” said William G. Mayer, a professor of political science at Northeastern University who has written extensively about swing voters. “I know Republicans who think that Trump is somehow incredibly savvy politically and knows just what he’s doing. I strongly disagree. I think he’s needlessly alienating a whole lot of people who might otherwise be inclined to vote for him.”

The Times poll found that undecided voters do not trust Mr. Trump to provide accurate information about the pandemic, and think he uses the presidential podium to promote falsehoods.

And in a finding that pollsters tend to watch closely (sometimes wisely, but sometimes not) for an indication of where a still far-off election might go, they believe the country is heading in the wrong direction.

As Mr. Trump has hewed to the right, Mr. Biden has shifted left, embracing, for example, the bankruptcy bill supported by Senator Elizabeth Warren of Massachusetts, who he defeated in the primary, and student loan forgiveness. But those positions, which once might have been ideological outliers, do not necessarily put Mr. Biden out of step with public opinion.

“I think Biden is much closer to where the country is, even though he’s moved to the left, than Trump is,” said Matthew J. Dowd, who was the chief strategist for the 2004 re-election campaign of Mr. Bush, but has since left the party.

“The country has moved to the left on guns, the country has moved to the left on race,” he said. “The country has more people of color.”

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Mr. Biden met with small business owners in Yeadon, Pa., earlier this month.Credit…Erin Schaff/The New York Times

Stanley Greenberg, a Democratic pollster who has long studied swing voters, said Mr. Trump’s options were limited as he seeks a second term because the Republican base was shrinking, marking the end of the dominance of the Tea Party.

“Essentially you’ve had a Tea Party revolt stopping the great majority of the country from governing for a decade,” he said. ”

“I think we are playing out the last battle,” he said. “I think this is ending a period in which the country has been gridlocked by Republican dominance.”

And even if Mr. Trump wanted to appeal to more swing voters, it can be complicated for a candidate to shift in such a polarized environment, where their every statement is under such scrutiny and voters can be dogmatic and unforgiving. “It’s much harder to do than it used to be,” said Anita Dunn, a senior adviser to Mr. Biden. “The polarization within parties. People won’t let you do it.”

Mr. Hazelwood said that even if was smart politically to try to appeal to the center in the final months of a general-election campaign, it may no longer be possible to do so.

“It’s hard to be in the middle,” he said. “If you try to take a middle ground with a group of people, you’re going to get attacked from both sides. So there’s no incentive to stand in the center and be a reasonable person. Your own side abandons you and the other side attacks you.”

Jon Hurdle, Matt Stevens, Kay Nolan and Kathleen Gray contributed reporting.

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