WASHINGTON (AP) — Their candidate may have lost the election, but President Donald Trump's supporters have no intention of fading away. After spending weeks amplifying Trump's unfounded claims that the November election was rigged against him, many of his loyal fans are eagerly awaiting his next ventures, including a potential presidential run in 2024.

In the meantime, they present a daunting challenge for President-elect Joe Biden: how to govern a bitterly divided nation that now includes many who not only disagree with his policies, but view him as an illegitimate president who won only because of mass election fraud, which did not actually happen.

"The effort by the Trump forces to delegitimize Biden has poisoned our political bloodstream so badly that it could take years to recover," said David Gergen, who served as an adviser to Presidents Richard Nixon, Gerald Ford, Ronald Reagan and Bill Clinton.

Trump will leave the White House on Jan. 20 with an iron grip on a Republican Party that has been transformed on his watch. Once known for its country club elites and embrace of military intervention and free trade, the GOP under Trump has become a populist party with an "America first" foreign policy that has alienated allies and fomented distrust in both international and domestic government institutions.

"I think the Republican Party today is the party of President Trump, and so his positions are the positions of the Republican voters," Sen. Mitt Romney, the 2012 Republican presidential nominee, recently told SiriusXM. The Utah senator said he believes Trump's "enormous influence" with the party is likely to wane to a certain degree as new faces step forward.

But among "those that are circling the 2024 race, beyond President Trump, it seems that many of them are headed in the same, more populist-oriented direction," he said.

In any case, Trump has no intention of ceding the spotlight as he openly flirts with running again in four years.

Trump will "loom very large over the Republican Party," predicted Alyssa Farah, until recently White House communications director. Don't expect Trump and Trumpism to "go off into the sunset," Farah says.

"He's got the most energetic base in modern political history," she said. "What the party is going to face is the reality that the president, even though it looks like he didn't win, got more votes than a Romney, than a McCain, than any Republican candidate in history. And we can't discount the voices of those 70 million Americans."

Exactly what Trump's post-White House future will look like is a work in progress.

He is expected to decamp to Florida with a small coterie of aides, where he will likely continue to use his Twitter bullhorn to reward allies and lash out at those who cross him as he mulls his next venture. That has put many of those eyeing taking on his mantle to run in 2024 in an awkward position.

"Look, he's the leader of this movement. No matter what happens in 2020, 2024 is there for his taking," White House press secretary Kayleigh McEnany said in a recent appearance on Fox News Channel. "His base is strong, they're not going away."

That also poses a conundrum for Biden, who will take an oath to lead a nation that appears more bitterly divided than at any time in modern history. Those divisions have only been exacerbated by Trump's campaign to cast doubt on the integrity of the election and overturn the will of the American people.

As a result, just 60% of Americans, including just 23% of Republicans, believe Biden's victory was legitimate, according to a recent Quinnipiac University poll.

Trump has repeatedly blamed his defeat on widespread voter fraud, despite the consensus of nonpartisan election officials that there wasn't any. Of the dozens of lawsuits the president and his allies have filed challenging election results, nearly all have been dismissed or dropped.

Gergen said the future of Trump's base will likely depend on a number of factors, including how the media cover him post-presidency and whether he becomes embroiled in legal troubles. He predicted Trump's actions will make it far harder for Biden to govern.

"It's going to be harder for a lot of Republicans to come to the negotiating table," Gergen said. He added that Trump's backers were likely to "keep a lot of pressure on mainstream Republicans not to break too often."

Charlie Sykes, a conservative talk radio host-turned-Trump critic who bemoaned Trump's efforts to de-legitimize Biden's election, sees the potential for long-term damage to trust in fundamental Democratic institutions.

"Trumpism is going to be a major force because he's both a cause and symptom of our division," Sykes said. "And he leaves behind him a legacy of real distrust, real divisions, Americans really not trusting one another, not trusting institutions."

Biden is well aware of the difficult road ahead in uniting a divided nation. But his aides have expressed confidence, pointing to positive signs like General Motors' recent decision to switch sides in its legal fight against California's right to set its own clean-air standards. And they voice hope that Biden may be able to appeal to some of Trump's working-class voters with priorities like bolstering American manufacturing and ensuring critical supplies are made in the U.S.

"We are realistic that there will always be folks who refuse to support the president-elect's agenda that more than 81 million Americans voted for. But that's not everyone," said Biden transition spokesman TJ Ducklo. "We believe there are a lot of Americans who voted for Donald Trump who just want their elected officials to deliver meaningful help during this once-in-a-generation crisis."

That will depend on people like Marthamae Kottschade, a self-described "Trumper" and member of "Trump's Front Row Joes," who traveled the county attending the president's campaign rallies.

Kottschade, who lives in Rochester, Minnesota, said she still has her Washington, D.C., hotel room booked for Inauguration Day and expects to see Trump sworn in again as president, even though Trump has no realistic path to overturn Biden's victory.

She said if Biden does end up in the White House, a lot of Trump supporters are ready to get more involved in politics at the local level before moving on to the next election.

"I know it's a movement. We firmly believe that as Trumpians," she said. "A year from now we may have Joe Biden as our president. ... We will have to accept it. This was the hand we were dealt with. And move on from there."

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Follow Colvin on Twitter at https://twitter.com/colvinj