From the outset of President Biden’s re-election campaign, the plan for winning was to make former President Donald J. Trump so unpalatable that voters uneasy with the incumbent would vote for him anyway.

But now Mr. Biden is stuck in a political tailspin, with an abysmal debate performance highlighting his inability to make a case against Mr. Trump and prompting a collective national hand-wringing about his ability to do his job while an increasing number of House Democrats say he should leave the race. To get voters to focus on the threats posed by a second Trump administration, Mr. Biden’s own allies say he first must escape his current doom loop and convince voters — even and especially fellow Democrats — that he is up to the job himself.

“The focus has to shift back to Trump and what rights we lose if he’s president,” said Representative Eric Swalwell of California, who ran against Mr. Biden for the 2020 Democratic presidential nomination. “The last three elections have shown us if you’re the focus, you lose.”

Indeed, the Biden campaign has long sought to make Mr. Trump its focus.

That’s why Mr. Biden kicked off this year with a blistering speech about Mr. Trump’s attempt to overthrow the last election, why his allies spent millions to block the No Labels effort and why the president has tried to highlight the anniversaries of news regarding abortion rights.

And it is why Mr. Biden’s top aides thought it was a good idea to move the first debate from September to June — to give voters the one-on-one look at Mr. Biden and Mr. Trump that the president’s team thought would recalibrate the race, lift Mr. Biden’s sagging poll numbers and remind voters what would change if Mr. Trump takes office again in January.

A pre-debate memo from Jen O’Malley Dillon, Mr. Biden’s campaign chair, mentioned Mr. Trump 18 times and Mr. Biden just five. Of Mr. Trump’s record, Ms. O’Malley Dillon wrote that the president “will hold Donald Trump accountable for all of it on the debate stage — and he’s raring to go.”