Sick with Covid and abandoned by allies, President Biden has been fuming at his Delaware beach house, increasingly resentful about what he sees as an orchestrated campaign to drive him out of the race and bitter toward some of those he once considered close, including his onetime running mate Barack Obama.

Mr. Biden has been around politics long enough to assume that the leaks appearing in the media in recent days are being coordinated to raise the pressure on him to step aside, according to people close to him. He considers Representative Nancy Pelosi, the former House speaker, the main instigator, but is irritated at Mr. Obama as well, seeing him as a puppet master behind the scenes.

The friction between the sitting president and leaders of his own party so close to an election is unlike anything seen in Washington in generations — especially because the Democrats now working to ease him out were some of the allies most critical to his success over the last dozen years. It was Mr. Obama who elevated Mr. Biden from a presidential also-ran to the vice presidency, setting him up to win the White House in 2020, and it was Ms. Pelosi and Senator Chuck Schumer, the Senate Democratic leader, who pushed through his landmark legislative achievements.

But several people close to Mr. Biden, who insisted on anonymity to discuss internal matters, described an under-the-weather president coughing and hacking hundreds of miles from the corridors of power as his presidency meets its most perilous moment.

He has watched with rising exasperation as a succession of news stories appeared, one after the other, reporting that Mr. Schumer, Ms. Pelosi, Mr. Obama and Representative Hakeem Jeffries of New York, the House Democratic leader, all had warned of a devastating defeat for the party in November.

And he certainly noticed that neither Mr. Obama nor former President Bill Clinton had done much to help him in recent days even as their own former aides publicly led the way in calling on him to withdraw in what were interpreted, rightly or wrongly, as messages from the former presidents’ camps. The unseen but clearly felt presence of Mr. Obama in particular has brought a Shakespearean quality to the drama now playing out, given their eight-year partnership.

While Mr. Biden and his team publicly insist that he is staying in the race, privately people close to him have said that he is increasingly accepting that he may not be able to, and some have begun discussing dates and venues for a possible announcement that he is stepping aside.

One factor that may stretch out a decision: Advisers believe that Mr. Biden would not want to do it before Prime Minister Benjamin Netanyahu of Israel visits Washington on Wednesday at the initiative of Republicans to address Congress, unwilling to give the premier the satisfaction given their strained relations lately over the Gaza war.

Yet Mr. Biden bristles at pressure and those pushing him risk getting his back up and prompting him to remain after all. Two people familiar with his thinking said he had not changed his mind as of Friday afternoon.

In privately railing about Mr. Obama and Mr. Clinton, Mr. Biden has made clear that he finds it particularly rich, as two people close to the situation put it, that the two presidents who were architects of historic Democratic losses in the 1994 and 2010 midterm elections would be lecturing him about how to save the party after he presided over a better-than-expected midterm in 2020. Another person said Mr. Obama’s suspected involvement has made it worse.

“We have to cauterize this wound right now and the sooner we can do it the better,” said Representative Gerald E. Connolly, Democrat of Virginia, who has not publicly called for the president to step aside. He said the barrage of criticism must be difficult for Mr. Biden. “I mean, to me, this is very painful. I think it just shows the cold calculus of politics.”

More congressional Democrats publicly called on the president on Friday to pass the torch to another candidate to take on former President Donald J. Trump in the fall. Among them were Senator Martin Heinrich of New Mexico and at least nine House Democrats, including Representative Zoe Lofgren, a close ally of Ms. Pelosi, her fellow Californian.

The fact that Ms. Pelosi’s allies have been coming out is seen as no coincidence at the president’s vacation house in Rehoboth Beach, Del. When another of her allies, Representative Adam B. Schiff of California, spoke out earlier this week, a Biden administration official noted that it might be Mr. Schiff’s lips moving, but it was Ms. Pelosi doing the speaking.

It has not just been her allies. Representative Seth Moulton, Democrat of Massachusetts and a Pelosi rival, said on Friday that Mr. Biden, “a mentor and friend” who had helped him get elected to the House in 2014, “didn’t seem to recognize me” when they met at the D-Day anniversary commemoration in France last month.

“Of course, that can happen as anyone ages, but as I watched the disastrous debate a few weeks ago, I have to admit that what I saw in Normandy was part of a deeper problem,” Mr. Moulton wrote in the Boston Globe, repeating his call for Mr. Biden to drop out.

Mr. Biden pushed back on Friday with a statement vowing to continue the race. “I look forward to getting back on the campaign trail next week to continue exposing the threat of Donald Trump’s Project 2025 agenda while making the case for my own record and the vision that I have for America: one where we save our democracy, protect our rights and freedoms, and create opportunity for everyone,” he said.

The White House and the Biden campaign have denied that he is about to drop out. “Absolutely, the president is in this race,” Jennifer O’Malley Dillon, the campaign chairwoman, said on MSNBC’s “Morning Joe” on Friday, one of the president’s favorite shows and a regular venue for Democrats speaking to other Democrats. “You’ve heard him say that time and time again.”

She acknowledged, though, that the campaign has seen erosion. “I’m not here to say that this hasn’t been a tough several weeks for the campaign,” she said. “There’s no doubt that it has been. And we’ve definitely seen some slippage in support, but it has been a small movement.” She argued that polls show the race was “hardened already” before the debate and so not that many voters have shifted since.

“The American people know that the president is older,” she said. “They see that. They knew that before the debate. Yes, of course, we have a lot of work to do to make sure that we are reassuring the American people that, yes, he’s old, but he can do the job and he can win.”

All of the political machinations were occurring as the president was fighting off symptoms from Covid in isolation in Rehoboth. He was still coughing and hoarse on Friday, but he was improving, according to his doctor. Jill Biden was with him, although staying in a separate room.

Among those with him in Rehoboth this weekend will be his aides Steve Ricchetti and Annie Tomasini. Anthony Bernal, the first lady’s chief of staff, accompanied her. It was unclear if Mr. Biden would still return to Washington on Sunday as planned, but he was tentatively scheduled to travel on Wednesday to Austin, Texas, for a postponed celebration of the 60th anniversary of the Civil Rights Act at the Lyndon B. Johnson Presidential Library.

Mr. Biden’s pique at his former partner, Mr. Obama, represents the latest chapter in a complicated relationship. While not close when they teamed up to run in 2008, they became friends over their two terms in the White House together, bonding especially when Mr. Biden’s son Beau died in 2015.

But Mr. Biden has nursed a grudge ever since Mr. Obama gently discouraged him from running for president in 2016, steering the Democratic nomination to Hillary Clinton, who lost to Mr. Trump. So Mr. Obama’s advice may not be particularly welcome in Rehoboth at this point, which is perhaps one reason the former president is not offering it directly, according to people close to him.

Mr. Obama last saw Mr. Biden at a lavish, record-setting Hollywood fund-raiser before the debate in June, when the two appeared onstage together. At the end, Mr. Obama appeared to be leading Mr. Biden offstage. One former Obama aide who was present that night said that it was clear that the former president was startled and shaken by how much Mr. Biden had aged and seemed disoriented.

That fund-raiser was the last big haul for the campaign, which had hoped to raise about $50 million this month from large donors for the Biden Victory Fund, just as it did in June. But after the debate, it may collect less than $25 million in July, an excruciatingly modest sum for a summer month in a presidential race, according to four people briefed on the campaign’s finances. The campaign is not required to disclose its July fund-raising numbers until mid-August, and a spokeswoman dismissed the reports as “speculation.”

As they try to influence Mr. Biden, many associates are holding back from harsh public statements because they feel empathy for him and worry such statements might backfire. Going public, some said, might cause the president to dig in even more. And some were reluctant to have their names attached to statements because they worry about his reaction to a pile-on from his friends.

While the roughly 40 members of Congress who have publicly called on the president to leave the race represents a minority, privately dozens more are said to agree. Two House Democrats estimated that on a secret ballot 70 percent to 80 percent of their caucus would prefer Mr. Biden to withdraw.

“They’re not going to be able to contain this. I think the dam has broken,” Mr. Connolly said. Even before Friday’s announcements, he said, “my sense was that a majority of my colleagues were so uneasy they would welcome a decision to change horses.”

Senator Chris Coons, Democrat of Delaware and one of the president’s closest allies, made an impassioned defense of his ability to serve a second term. Speaking from the stage of the Aspen Security Conference in Colorado, Mr. Coons cited the president’s work hosting a NATO summit as well as his recent news conference and campaign events. “There are folks still saying he is not strong enough or capable enough to be our next president,” Mr. Coons said. “I disagree.”

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