Mr. Trump’s deepest hostility is reserved for Gov. Brian Kemp of Georgia, advisers said, and they expect he will expend the most energy trying to damage Mr. Kemp’s re-election bid. The governor’s original sin was in choosing Kelly Loeffler over Mr. Trump’s favored candidate, Doug Collins, to fill a vacant Senate seat in 2019, but it evolved into something more consuming as Mr. Trump repeated his debunked claims of widespread fraud in the state and held Mr. Kemp responsible for not doing enough to challenge the election results.

Mr. Collins, a hard-line Trump backer, hasn’t decided whether to challenge Mr. Kemp or seek the Republican nomination against Senator Raphael Warnock, the Democrat who defeated Ms. Loeffler in a special election and will face voters again in 2022, or if he will choose not to run for anything, a Collins aide said Monday.

Next on Mr. Trump’s personal hit list is Representative Liz Cheney, the Republican from Wyoming, people close to him said. Ms. Cheney was the only member of the House G.O.P. leadership to vote to impeach. It’s unclear whether Mr. Trump will target her seat, or simply her leadership post in the House, but advisers said they anticipate he will take opportunities to damage her.

Sarah Longwell, the executive director of the Republican Accountability Project, an anti-Trump group, said she and her colleagues plan to raise and spend $50 million to defend the 10 pro-impeachment House Republicans in primary contests and attack those who voted to object to the Electoral College results after the Jan. 6 riot at the Capitol. She said the group would aim to defeat Mr. Jordan in an Ohio Senate primary if he runs against an establishment-minded Republican.