Senator Richard M. Burr’s decision to vote for the conviction of former President Donald J. Trump on Saturday added fuel to speculation that Lara Trump, Mr. Trump’s daughter in-law, will seek the North Carolina Senate seat Mr. Burr will vacate in 2022.

Senator Lindsey Graham of South Carolina, a former Trump critic turned stalwart defender, on Sunday predicted that Mr. Burr’s somewhat surprising dissent would prompt a revolt from the right that would result in the election of more pro-Trump candidates.

“My friend Richard Burr just made Lara Trump almost the certain nominee for the Senate seat in North Carolina to replace him if she runs,” he said in an interview on Fox News.

Ms. Trump, 38, a former personal trainer and television producer who grew up in Wilmington, on the coast, has been floating herself as a possible Burr successor for months.

She did not immediately respond to a request for comment. One senior Republican official with knowledge of her plans said the Jan. 6 riot soured her on running, but said Ms. Trump would decide over the next few months if she would run as part of a coordinated Trump family comeback.

Another Republican, former Representative Mark Walker, a Trump ally, has already announced his candidacy, and Pat McCrory, a Republican former governor, is also a possible candidate. Mark Meadows, the former North Carolina representative and former Trump chief of staff, is also said to be in the mix.

“We are going to take a very long look at all the candidates versus, you know, some kind of coronation,” said Mark Brody, a member of the Republican National Committee from Union County, outside Charlotte.

Doug Heye, a former R.N.C. spokesman who used to work for Mr. Burr, questioned whether Ms. Trump was willing to endure the tussle and tedium of running or serving. “Many people love the speculation and the attention, but being senator is a lot of hard work,” he said.

Then there is the question of residence. Ms. Trump currently lives with her husband, Eric, and their children in the northern suburbs of New York City and would have to move back.

If she runs, the Trump family might be a liability in a battleground that the former president won by a mere 1.3 percentage points in 2020 — or it might confer no advantage at all, depending on the political environment in 2022.

“There is a myth that Trump voters will come out for Trump candidates or family members,” said John Anzalone, a Democratic pollster who has worked on campaigns in the South. “Cult members only come out in full force for the cult leader.”

And Ms. Trump’s candidacy could help increase Democratic turnout, especially among the state’s large Black population, countering the typical falloff experienced in most midterm elections.

But Ms. Trump’s boosters, led by Mr. Graham, are hoping she can use the backlash in the party’s base to catapult her to the front of the field.

After Mr. Burr’s vote, the North Carolina Republican Party rebuked Mr. Burr, calling his vote “shocking and disappointing.”

Representative Patrick T. McHenry, a Republican who serves in a leadership position in the House minority, downplayed the importance of Mr. Burr’s vote.

But he said Ms. Trump would “be the odds-on favorite” if she runs, adding, “No one comes close.”