A stunning new poll Tuesday showed Donald Trump has reclaimed the lead from Democratic opponent Hillary Clinton, becoming the latest survey to suggest the GOP presidential nominee has put a bad month behind him.

Republicans on Capitol Hill said they’re increasingly hopeful of Mr. Trump’s chances in November, saying he’s done a better job of making the election about Mrs. Clinton — whose negative image remains a hurdle on her path to the White House.

The latest CNN/ORC survey, released Tuesday morning, showed Mr. Trump with a 2-percentage point lead in a national four-way race among likely voters with Mrs. Clinton, Libertarian hopeful Gary Johnson and Green Party nominee Jill Stein.

Pollsters cautioned that the CNN poll seemed skewed toward Republicans, but with a spate of other recent surveys also showing Mr. Trump within the margin of error, Mrs. Clinton’s post-convention bump has dissipated.

The latest Real Clear Politics average has Mrs. Clinton leading Mr. Trump head-to-head by just 2.4 points, which is down from the nearly double-digit advantage she held a month ago.

Mr. Trump, speaking at a rally in Virginia Beach, said the new polling has boosted his fellow Republicans’ morale. “It’s good psychology,” he said. “People that didn’t call me yesterday, they’re calling me today.”

Mrs. Clinton’s aides, meanwhile, said polling over the Labor Day weekend might have skewed the results, but said Mrs. Clinton isn’t paying attention to polls anyway.

“Every single poll that comes out — we never take anything for granted and we assume it’s going to be close,” Clinton spokeswoman Kristina Schake said on MSNBC.

The CNN poll came the same day as an NBC News/Survey Monkey poll that gave Mrs. Clinton a 4-point lead, while a Los Angeles Times/University of Southern California survey of Mr. Trump head-to-head with Mrs. Clinton showed them tied at 44 percent apiece.

One explanation for Mr. Trump’s lead in the CNN poll is that the lead covered the sample of “likely voters.” When the registered voters — those who are eligible but aren’t certain to cast ballots — were sampled, Mrs. Clinton held a 3-point lead.

It’s a delicate dance that pollsters do as the election nears, and as much art as science — trying to determine who is likely to vote and to weed out those casual voters who are likely to stay home and thus won’t affect the outcome.

“As a general rule, you’re screening out people like younger people and minorities who sometimes have a lower voter participation rate who are generally predisposed to vote Democratic,” said David Paleologos, director of the Suffolk University Political Research Center.

Some pollsters ask voters’ intent to cast a ballot this year, while other surveys judge likely voters based on how they describe their history of voting.

“What I have discovered over the years is that you can frequently outsmart yourself,” said Republican pollster Whit Ayres. “The way we define it is, if someone tells you they are absolutely certain, very likely or somewhat likely to vote, then we will keep them in the sample.”

In looking at CNN’s poll, quite apart from the broader issue of determining likely voters and the resulting Republican advantage, Mr. Ayres said it also appeared to oversample Republicans when compared to historic party identification trends. Still, he said it’s clear Mr. Trump has made up ground on Mrs. Clinton.

He said Mr. Trump’s best path to victory is now to drive up numbers among white voters in Great Lake states like Ohio, Pennsylvania, Wisconsin and Michigan.

Mr. Ayres said things are “hopeless” for Mr. Trump among blacks and Hispanics but that he could cajole reluctant GOP-leaning moderate white voters if he stops vilifying racial minorities. He said, broadly speaking, a lower overall turnout in November wouldn’t necessarily benefit Mr. Trump.

“It depends who turns out on the low side,” Mr. Ayres said. “As a general rule, the lower turnout of midterms helps Republicans. But it’s got to be a lower turnout that looks like a midterm electorate, rather than a presidential election electorate, which traditionally draws much higher proportions of young people and nonwhites than do midterm elections.”

When the CNN survey went from the registered to the likely voter screen, Mr. Trump increased his lead over Mrs. Clinton among white voters from 17 points to 21 points. Among white noncollege graduates, his lead increased from 35 points to 44 points.

Republicans likeliest to vote also appeared to be more supportive of Mr. Trump. His share of the GOP vote increased to 90 percent among likely voters, from 85 percent among registered voters, while Mrs. Clinton’s support among Democrats ticked up 2 points, from 90 percent to 92 percent.

As Mr. Trump’s numbers improve, so do GOP lawmakers’ spirits. Sen. John Cornyn of Texas, the second-ranking Republican in the Senate, said it could help down the ticket, where the battle for control of the Senate is fierce.

“I am glad to see the gap shrink between Trump and Clinton, because that makes the job a little easier on people like Mark Kirk and Kelly Ayotte and Ron Johnson, Pat Toomey and Rob Portman, among others; and Joe Heck, Marco Rubio and all of our other candidates. You can’t overcome insurmountable headwinds if you are a downballot race. So that is another reason why … we need to win or at least stay very close.”

⦁ S.A. Miller and Seth McLaughlin contributed to this article.

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