Trump Lost the Race. But Republicans Know It’s Still His Party.

The election of 2020 ended for Republican Party leaders a lot like the election of 2016 began: As much as they may want to move on from Donald J. Trump, he won’t let them — and neither will the voters.

After losing the White House to Joseph R. Biden Jr. and the popular vote in seven presidential elections since 1980, and facing the possibility of defeat in Arizona and Georgia where losses were once unthinkable, Republicans were grappling with how to untangle the man from a movement that is likely to dictate party politics for years.

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From inside Senate offices, think tanks and over off-the-record salons on Zoom, the conversations about what’s next have grown in urgency now that the final months of the Trump presidency are at hand.

“He is sort of the king with no heirs,” said Oren Cass, the executive director of American Compass, a group that hosts monthly online happy hours of Capitol Hill staff and policy experts to debate the successes and failures of the Trump agenda. Mr. Cass said Mr. Trump’s defeat set up a clash between more conventional Republicans who, on the one hand, took the attitude that “this too shall pass, and we can go back to doing to what we were doing before,” and those who think the president “called attention to a certain set of issues and voters that certainly the center-right wasn’t paying enough attention to.”