WASHINGTON — Despite a week of campaign stops, interviews, and insistence that he is the best candidate to confront President Trump, President Biden has done little to soften the push for him to exit the 2024 race.

Mr. Biden has weighty options before him this weekend that could set the direction of the country and his party as the nation heads toward the November election with an energized GOP after the Republican nominating convention to send Trump back to the White House.

Almost 35 Democrats in Congress say it’s time for Mr. Biden to quit the race — 12 coming forward on Friday alone — with more lawmakers expected to speak out in the days ahead. Donors have raised concerns. And an organization calling on Mr. Biden to “Pass the Torch” planned a rally Saturday at the White House.

“There is no joy in the recognition he should not be our nominee in November,” said Representative Morgan McGarvey of Kentucky, one of the Democrats urging his exit from the race. “But the stakes of this election are too high and we can’t risk the focus of the campaign being anything other than Donald Trump.”

The standoff has become increasingly untenable for the party and its leaders, a month from the Democratic National Convention that should be a unifying moment to nominate their incumbent president to confront Trump. Instead the party is at a crossroads unseen in generations.

It’s creating a stark juxtaposition with Republicans who, after years of bitter and chaotic infighting over Trump, have essentially embraced the former president’s takeover of the GOP, despite his criminal conviction in a hush money case and pending federal criminal indictments for trying to overturn the 2020 election before the January 6, 2021, attack on the Capitol.

From his beach home in Delaware, Mr. Biden, 81, is isolating with a Covid infection, but also politically with a small circle of family and close advisers. White House doctor Kevin O’Connor said Friday that the president still had a dry cough and hoarseness, but his Covid symptoms had improved.

The president’s team insisted he’s ready to return to the campaign this coming week to counter what he called a “dark vision” laid out by Trump.

“Together, as a party and as a country, we can and will defeat him at the ballot box,” Mr. Biden said in a statement Friday. “The stakes are high, and the choice is clear. Together, we will win.”

Yet outside the Rehoboth enclave the debate and passions are intensifying.

A donor call with some 300 people Friday was described as a waste of time by one participant, who was granted anonymity to discuss the private conversation. While the person was complimentary of Vice President Harris, who spoke for five minutes, the rest of the time was filled by others who brushed aside donor concerns, according to the participant.

Not only are the Democrats split over whether Mr. Biden should stay in the race or step aside, they also lack consensus about how to choose a successor.

Democrats who are agitating for Mr. Biden to leave do not appear to have coalesced around a plan for what would happen next, for now. Very few of the lawmakers have mentioned Ms. Harris in their statements, and some have said they favor an open nominating process that would throw the party’s endorsement behind a new candidate.

Senators Tester of Montana and Welch of Vermont have both called for Biden to exit the race and said they would favor an open nominating process at the convention.

“Having it be open would strengthen whoever is the ultimate nominee,” Mr. Welch said in an interview with the Associated Press.

Other Democrats say it would be politically unthinkable to move past Ms. Harris, the nation’s first woman vice president, who is Black and Southeast Asian, and logistically unworkable with a virtual nominating vote being planned for early next month, before the August 19 Democratic convention at Chicago.

Representative Betty McCollum of Minnesota, who is among those who called on Mr. Biden to step aside, explicitly endorsed Ms. Harris as a replacement.

“To give Democrats a strong, viable path to winning the White House, I am calling upon President Biden to release his delegates and empower Vice-President Harris to step forward to become the Democratic nominee for President,” Ms. McCollum said in her statement.

It’s unclear what else, if anything, the president could do to reverse course and win back lawmakers and Democratic voters, who are wary of his ability to beat back Trump and serve another term after his halting debate performance last month.

Nearly two-thirds of Democrats say Mr. Biden should withdraw from the presidential race and let his party nominate a different candidate, according to a new AP-NORC Center for Public Affairs Research poll, sharply undercutting his post-debate claim that “average Democrats” are still with him even if some “big names” are turning on him.

At the same time, a majority of Democrats believe Ms. Harris would do a good job in the top slot, according to a separate AP-NORC Center for Public Affairs Research poll.

Mr. Biden, who sent a defiant letter to Democrats in Congress in the initial aftermath of his debate performance vowing to stay in the race, has yet to visit Capitol Hill to shore up support, an absence noticed by senators and representatives.

Mr. Biden still has strong backers. He picked up support Friday from the Congressional Hispanic Caucus’ campaign arm and has backing from leaders of the Congressional Black Caucus and the Congressional Progressive Caucus.