The push among some Democrats to replace President Biden as the Democratic nominee is getting a boost from new polling even as Mr. Biden signals that he’s getting impatient with Democrats trying to change the top of the ticket.

A new survey from the Associated Press and the NORC Center for Public Affairs Research found that 65 percent of Democratic respondents say that Mr. Biden should withdraw from the race.

Another 77 percent of independents say Mr. Biden should withdraw and, among all voters, 70 percent of all respondents say he should withdraw.

Overall, 57 percent of respondents said that President Trump should withdraw from the race. Only 26 percent of Republicans, though, said they would prefer another candidate.

Among Democrats, Black voters were the most supportive of Mr. Biden, with 49 percent saying he should drop out and 50 percent saying he should stay in the race. For comparison, 67 percent of white Democrats and 64 percent of Hispanic Democrats said he should drop out.

The survey was conducted between July 11 and July 15, meaning after Mr. Biden’s poor debate performance but before the attempt on Trump’s life. The survey of 1,253 American adults had a margin of sampling error of plus or minus 3.8 points.

The survey results come as efforts to oust Mr. Biden begin to spin up again after taking a pause in the wake of the assassination attempt against Trump.

Politico reports that a former House speaker, Nancy Pelosi, is quietly collecting comments from Democratic House members with regard to Mr. Biden’s ability to win and his potential effects on down-ballot races.

It also comes as Mr. Biden signals that he is growing impatient with Democratic efforts to convince him to step down, with NBC News reporting that Mr. Biden is tightening his inner circle and attempting to pivot the internal party conversation back to how he can defeat Trump in November.

“You made me the nominee. No one else. Not the press, not the pundits, not the insiders, not donors,” Mr. Biden said at a campaign event in Detroit Tuesday. “And I’m not going anywhere.”

Overshadowing that conversation, however, is the reality that Democrats might fare better on the presidential level and in down-ballot races if Mr. Biden was to step aside and let a younger candidate run at the top of the ticket.

A new BlueLabs Analytics survey circulating in Democratic circles and obtained by Politico found, “Alternative Democratic candidates run ahead of President Biden by an average of three points across the battleground states.”

“Nearly every tested Democrat performs better than the President. This includes Vice President Harris, who runs better than the President (but behind the average alternative),” the polling memo reads.

To conduct the survey, the pollster contacted 15,000 voters across Wisconsin, Michigan, Pennsylvania, Nevada, Arizona, North Carolina, and Georgia, making it one of the surveys with the largest sample size on the issue.

The survey found that Senator Kelly and Governors Moore, Shapiro, and Whitmer were the best-performing Democrats in their polling results, outpacing Mr. Biden by about five points across the swing states, though the memo does not include top-line numbers against Trump.

“An average of almost 3 percent of Trump voters in a Trump/Biden matchup switch to voting Democrat when an alternative candidate leads the ticket,” the memo reads. “Just 1 percent of Biden voters defect to Trump when presented with an alternative Democratic candidate.”

The polling memo also reports that young voters, independents, and voters who haven’t voted since 2020 were the most likely to say that nominating someone other than Mr. Biden would increase their support for the Democratic candidate.

The most prominent Democrat in the House to call on Mr. Biden to step aside came Wednesday, when Congressman Adam Schiff said it was time for Mr. Biden to bow out.

“While the choice to withdraw from the campaign is President Biden’s alone, I believe it is time for him to pass the torch,” Mr. Schiff said in a statement. “And in doing so, secure his legacy of leadership by allowing us to defeat Donald Trump in the upcoming election.”