President Biden is cruising to the Democratic nomination. Former President Donald J. Trump could begin to wrap up his party’s nod within days.

America’s response: This can’t be real.

Even as both men stroll toward likely summer coronations and a fall rematch, an undercurrent of disbelief is coursing through the country. Many Republicans view Mr. Biden as so politically and physically weak that they think his party will replace him. Many Democrats can’t fathom that Mr. Trump could win another nomination while he is facing 91 felony counts and four criminal trials.

This incredulity — ranging from casual doubtfulness to conspiratorial denial — has lurked beneath a year of polling showing a deeply gloomy public mood, and has emerged in dozens of interviews over the past two weeks as well as recent declarations from candidates and political commentators.

“They’ll pull a switcheroo at the last minute,” David Lage, a Republican missionary from Spring Hill, Iowa, said of Democrats. “They’ve tried about every other dirty trick.”

Paige Leary of Exeter, N.H., an independent who voted for Mr. Biden in 2020 and for Democrats in previous presidential elections, also questioned whether Mr. Trump would be the Republican nominee.

“The jury’s out,” she said. “We don’t know what will happen legally with Trump.”

Such contrasting views reflect how the doubts about Mr. Biden and Mr. Trump have different origins in each party.

For Republicans, waning trust in the political system is the dominant theme. The party is nearly a decade into the Trump era, and misinformation and conspiratorial thinking about Mr. Biden’s health and Democratic plotting to replace him are rampant in the conservative news media and broader political world. A favorite, and entirely baseless, theory is that Michelle Obama will seize his spot in a Democratic coup.

Democrats, for their part, are consumed by a gut-wrenching hope that Mr. Trump won’t be the nominee. They are crossing their fingers that his legal cases or efforts to disqualify him from office through the 14th Amendment will keep him off the ballot. Most harbor few hopes that his nomination can be derailed; they are simply clinging to a belief that a man they loathe will somehow go away.

In the muddy middle, too, are more casual voters who are not yet paying attention to an election nearly a year away, but believe that surely the nation will find someone new.

“People in both parties really dislike the likely nominee of the other,” said Charles Franklin, the director of the Marquette Law School Poll. He said he had heard enough people suggesting that Mr. Trump and Mr. Biden would be displaced that he included a question about it on polls he is conducting this month.

“Voters who think, ‘Goodness please, let’s not have a rerun of 2020,’ will realize that we are tuning into another episode,” Mr. Franklin said. “Same characters, similar plotline. Get used to it.”

The Biden campaign’s internal data has found that nearly three-quarters of its so-called targeted voter universe does not believe Mr. Trump will be the Republican nominee. Those voters are a broad set of Americans who are not plugged into the news and don’t currently support the president’s re-election, but the campaign believes they can be persuaded to do so.

But Mr. Biden and his team are running up against a barrage of wild speculation from Republicans.

“I personally don’t think he makes it,” Mr. Trump said of Mr. Biden on Fox News last month. Mr. DeSantis suggested at a Fox News town-hall event last week that Democrats “may sub him out for someone else.”

The commentator Megyn Kelly floated the theory about Ms. Obama on her podcast last week, and the right-wing host Tomi Lahren said on her internet show on Wednesday that Democrats would sub in Gov. Gavin Newsom of California.

“I continue to predict — as I have for well over two years — that Michelle Obama will be the Democrat Party Nominee for President in 2024,” Roger J. Stone Jr., the longtime adviser to Mr. Trump, posted on social media a week before the Iowa caucuses.

Even though Ms. Obama has repeatedly ruled out any presidential interest, OddsChecker, an online bookmaker, on Friday gave her nearly even odds of winning the presidential election with Nikki Haley, the former South Carolina governor who placed third in Iowa on Monday. Both were behind Mr. Trump and Mr. Biden. The site put Mr. Newsom in fifth place, well ahead of Mr. DeSantis.

Many of these beliefs stem from the Trump-inspired right, which has trafficked in all manner of false claims about the 2020 election and is ready to believe the fix will be in again for 2024. The overarching, bizarre notion is that the Democratic Party is acting at the whims of the “deep state” and has already concocted its plan to replace Mr. Biden.

And there are conspiracy theories within the conspiracy theories.

Several Republicans interviewed at recent presidential campaign stops repeated a decade-old, anti-transgender falsehood about Ms. Obama propagated by the disgraced conspiracy theorist Alex Jones.

“I think Michelle Obama — or Michael Obama — will be it for the Democrats,” said Sue Grove, a secretary from Van Meter, Iowa, who works for Republican legislators at the Iowa State Capitol and supported the entrepreneur Vivek Ramaswamy for president before he dropped out. “I have also heard rumblings about Oprah. I don’t know how Biden could get in again.”

Far-right online circles are also rife with baseless theories that Democrats could bring about an untimely death for the 81-year-old president. Ms. Grove darkly alluded to that idea: “You know, there’s a lot of Democratic suspicious deaths, sudden deaths,” she said. “There’s a lot of suicides, right?”

Other conjecture is not nearly so violent.

Some Republicans predict that Mr. Biden will be removed at the Democratic National Convention in August in Chicago. They note that in 2020, leading Democrats united quickly behind Mr. Biden to stop Senator Bernie Sanders of Vermont — and insist that it wouldn’t be so far-fetched to see the party now turn on its politically vulnerable president.

“I don’t think Biden will hold up,” said Amy Meyer, a Republican data analyst who served as an Iowa caucus captain for Mr. DeSantis. “The Democrats have their super delegates and so they don’t have a democratic primary process. So I think they’ll just do what they want.”

No prominent Democrats have argued that Mr. Trump won’t be the Republican nominee. Indeed, part of Mr. Biden’s immediate polling problem, his advisers say, is that voters who dislike Mr. Trump have not realized how likely he is to win the nomination.

The left, alarmed at the prospect of a second Trump presidency, is looking to the legal system for salvation, hoping that prosecutors will put a stop to his political juggernaut. Or, if not a criminal jury, then perhaps the Supreme Court, which Democrats hope will uphold the decisions of two states to bar Mr. Trump from the ballot under the 14th Amendment.

“It seems like there’s a mass delusion about Trump,” said Bill Schafer, a renewable energy executive from Boulder, Colo., who described himself as a former Republican who voted for Mr. Biden in 2020. He said he had not been able to accept that Republicans would nominate Mr. Trump.

“I turned on Fox News to see, How does it feel to live in this world?” he said. “This is a combination of The National Enquirer and professional wrestling. If you can believe in those two things, then MAGA is a piece of cake.”

Convincing voters that Mr. Trump will be on the ballot come November is in fact central to Mr. Biden’s electoral strategy. Campaign officials say that his political standing will improve once the reality of Mr. Trump’s likely renomination sets in with voters not following the race closely.

“This isn’t a hypothetical,” Ammar Moussa, a Biden campaign spokesman, said. “The president looks forward to spending the next 10 months reminding the American people how dangerous Donald Trump and his MAGA agenda are.”

And then there are the voters who are still trying to wish into existence some other 2024 matchup.

Yoram Ariely, a wealthy Democrat who is retired from importing and exporting fruit juice concentrates, took it upon himself to commission an October poll from SurveyUSA asking voters if they would prefer that Mr. Biden quit his presidential campaign and run for vice president instead.

Using that biased and implausible question, the poll found that among 1,024 Democrats, 69 percent believed Mr. Biden would be better off trying to reclaim the office he held for eight years while Barack Obama was president.

Mr. Ariely said he had subsidized the poll to help persuade Mr. Biden and other Democrats that the president should find something to do other than seek re-election. So far, that proposal hasn’t gotten much traction.

“If he would step down clearly and cleanly, it would be for the best,” said Mr. Ariely, who splits his time between upstate New York and Florida. “My suggestion is for him to do the right thing and find an exit ramp.”

Shane Goldmacher, Neil Vigdor and Alyce McFadden contributed reporting.

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