In the wee hours of Friday morning, not long after President Biden had walked off the stage from a disastrous debate, his campaign chair, Jen O’Malley Dillon, acknowledged in a series of private calls with prominent supporters that the night had gone poorly but urged them not to overreact.

Later on Friday, top White House aides worked the phones, with Mr. Biden’s chief of staff, Jeff Zients, calling the Democratic leader of the Senate, Chuck Schumer, to check in, according to a person familiar with the call. And by the afternoon, the Biden campaign had transformed its weekly all-staff call into a virtual pep talk to dispel any doubts creeping into the campaign offices in Wilmington, Del., and beyond.

“Nothing fundamentally changed about this election last night,” said Quentin Fulks, Mr. Biden’s deputy campaign manager, according to a recording of the all-staff meeting. “We’re going to get punched. We’re going to punch back. We’re going to get up when we get punched.”

The 48 hours after the debate were a frenzied campaign within a campaign to save Mr. Biden’s suddenly teetering candidacy, a multiday damage-control effort to pressure and plead with anxious Democratic lawmakers, surrogates, activists and donors to stand by the president, the party’s presumptive nominee.

After a frenetic run of seven campaign events across four states since the debate, Mr. Biden himself is taking a pause for a preplanned family gathering at Camp David. He arrived late on Saturday and will be joined by his wife, Jill Biden, the first lady, as well as the Biden children and grandchildren, according to two people familiar with the scheduling.

The gathering, for a family photo shoot, was scheduled in the spring, according to those people. But the timing and circumstances of Mr. Biden being surrounded by the very family members who have been crucial in his past decisions to run for the presidency — or to sit out a race — have heightened the stakes and scrutiny surrounding the Camp David retreat.