With President Biden under pressure to drop his bid for a second term, his party has been thrust into uncharted territory, struggling with a long list of risks and rewards as it faces the prospect of replacing Mr. Biden less than two months before the party convention.

No presumptive nominee has withdrawn this late in the process. But no party has faced the challenge the Democrats face today: a nominee dogged by doubts about his mental acuity; his ability to beat his rival, former President Donald J. Trump; and his fitness to serve another four years as president.

All of this has left Democrats struggling with critical questions: Is it easier to defeat Mr. Trump with or without Mr. Biden at the top of the ticket? Is it riskier to go with a new candidate or stick with a president who appears headed for defeat?

On Wednesday, a New York Times/Siena College poll found that Mr. Trump’s lead over Mr. Biden among likely voters had grown to six percentage points after the president’s halting debate performance last week.

The White House said the president was not dropping out, and he met with Democratic governors on Wednesday. But he confided to at least two allies that he realized the next few days were crucial to saving his candidacy. To that end, Mr. Biden began preparing for his first sit-down interview since the debate, with George Stephanopoulos of ABC News, on Friday morning.

Several Democrats said that no matter the risks, a new nominee could bring a host of benefits to the party, particularly if Mr. Biden anointed a successor in an effort to assure a smooth transition and minimize intraparty battling.

A new-generation candidate could bring a jolt of energy to the ticket. It would give so-called double haters, voters unhappy with the rematch between an 81-year-old president and a 78-year-old former president, a possible new place to go this November. A new candidate would almost certainly benefit from a surge of campaign contributions, at least initially.

“If you are driving your car straight off a cliff, there are definitely risks to swerving right or left instead,” said Howard Wolfson, a Democratic consultant, who said he was doubtful that Mr. Biden could recover from the debate and go on to defeat Mr. Trump.

But other Democrats, including some advising Mr. Biden, said that changing horses now could lead to divisive and destructive feuding in the party. It could saddle the party with an untested candidate and a logistical nightmare that would only increase the prospects of a Trump victory this fall.

“A lot of things have to fall into place where it would take an act of God for it to go well,” said Stephanie Cutter, a Democratic consultant who also advises the Biden campaign but was not speaking on its behalf.

The Crash-Course Campaign

A late-stage Biden replacement would be less known and less experienced on the national stage than either Mr. Biden or Mr. Trump — obstacles that a newly selected nominee would have to quickly navigate.

Without a traditional primary, the candidates would be deprived of on-the-ground lessons in being a presidential candidate: drilled with questions from voters, learning the details of unfamiliar regional issues and of making alliances with key players of each state. And they would not be subject to a thorough vetting and examination — by the voters, their opponents and the media — of their records and political strengths and weaknesses.

Political leaders have seen the risks of turning to unknown candidates in last-minute vice-presidential selections: Sarah Palin of Alaska, who was John McCain’s running-mate in 2008, and Dan Quayle of Indiana, who was George H.W. Bush’s running mate in 1988, both struggled and stumbled their way through their election seasons.

“Picking someone new is not without substantial risk — which is why so many Democrats are so reluctant to consider replacing Joe Biden on the ticket,” said Steve McMahon, a Democratic strategist who worked on the presidential campaign of former Governor Howard Dean of Vermont in 2004.

Republicans would not make it easy. In normal circumstances, a campaign has months to do opposition research on its own candidate to make sure it is prepared for any attack.

But the Trump campaign has already had ample time to assemble opposition research files of potentially damaging information on Mr. Biden’s potential successors, which it could use to define them before they have a chance to do so themselves.

(“Is Invasion Czar Kamala Harris the Best They Got?” the Trump campaign asked in an email sent Wednesday morning, a bullet-point assembly of attacks, including on her role in Mr. Biden’s immigration policy.)

That said, the sheer excitement of a new face — in a year when so many voters have been complaining about the rerun of 2020 — could provide a real lift going into the fall campaign. And while a new candidate may be subject to damaging opposition research findings by Mr. Trump, there is less time for that information to be aired and to sink in.

A Fraught Process

There is no real playbook on how to replace a candidate who drops out weeks before the convention. For some Democrats, the potential disarray and division are reason enough for Mr. Biden to stay in the race.

One way to minimize the disruption could be for Mr. Biden to endorse Vice President Kamala Harris on his way out, some Democrats argue.

“The advantage that Kamala Harris holds in this hypothetical is that she has already been vetted — thoroughly,” said Elaine Kamarck, a member of the Democratic National Committee and a fellow at the Brookings Institution. “We probably know everything there is to know about her. Which can’t be said for others. And she has been in the White House for four years. She has plenty of name recognition.”

If Mr. Biden didn’t name his preferred successor, should he leave the race, the process would become a fight for delegates’ loyalties, one that would be likely to expose ideological and generational struggles that have been brewing for years. Fights over the war in Gaza, immigration or policing, already expected to play out at the convention, could now become far more important, helping to determine the new nominee.

One thing Democrats should never take for granted is that “Democrats can agree on something,” said Ms. Cutter.

But that is far from a unanimous view. Ms. Kamarck said that the animosity Democrats feel toward Mr. Trump would bring them together.

“The antipathy toward Donald Trump’s second term from four years ago hasn’t changed,” she said.

And some Democrats said there were ways to minimize lasting damage. Jeff Weaver, a strategist for Senator Bernie Sanders’ two presidential campaigns, said the party should settle on a fast-track selection process, including party-sanctioned debates.

“If it were to happen, it would consume all the political oxygen in the room until the Democratic convention,” he said. “And by the time of the convention, people would have a very good sense of who these candidates are.”

A new nominee could face other complicating factors. An Ohio election law requires parties to have their candidates set by Aug. 7, nearly two weeks before the Democratic National Convention in Chicago. The party had been planning to formalize Mr. Biden’s nomination before then, through a virtual online roll call vote. Barring a change to the law, which may still happen, the party will be hard pressed to settle on its new ticket by that August deadline — or give up being on the ballot in Ohio.

In other states, Republicans are already considering using lawsuits to block Democrats from changing the name of the nominee on ballots.

Richard Winger, an expert on ballot rules who is the publisher of Ballot Access News, said he did not think such litigation could legitimately interfere with the ballots in the states.

A Scramble for Cash

A new Democratic nominee would be likely to inherit the Biden campaign infrastructure, the party infrastructure and organizations already set up in swing states, party strategists said.

But that will get that person only so far without ample cash flow. A new candidate would need to raise hundreds of millions of dollars to mount a serious campaign and introduce themselves to America in an abbreviated campaign.

“Do they have $1 billion to do it, and do they have the time to spend $1 billion to tell this story?” said Cornell Belcher, a Democratic pollster who argues that switching candidates would be a bad idea for the party.

The answer in part depends on whether this candidate is Ms. Harris.

Saurav Ghosh, the director of campaign finance reform at the Campaign Legal Center, said that as vice president Ms. Harris would be able to take over Mr. Biden’s campaign accounts if she became the nominee, where others would not.

If the new nominee is not Ms. Harris, Mr. Biden’s war chest could revert to the Democratic National Committee, which could spend only $32 million of that in coordination with the campaign.

Several top Democratic strategists said they were not concerned about that challenge. The new candidate’s coffers would probably be flooded with online donations from rank-and-file supporters. Better still, donors who had given the maximum amount to Mr. Biden — and could therefore not give more to Ms. Harris — would have a clean slate to give maximum donations all over again to a different nominee, a potentially huge windfall.

Also, the Democrats’ array of well-financed super PACs — which can raise and spend unlimited sums, but may not legally coordinate with campaigns as they do so — would almost certainly shift quickly to back a new nominee.

Still, the supporters of Mr. Biden who oppose the idea of a change said it would not be as easy to fire up a new campaign as those pushing for one may think.

“You can’t snap your finger and assume it materializes,” said Gov. Phil Murphy of New Jersey, who insisted Mr. Biden would be the nominee in the fall.