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

South Carolina Senator Lindsey Graham, a former Trump critic turned strong defender, predicted Sunday that Mr. Burr’s somewhat surprising dissent would spark a right-wing riot that would lead to the election of more pro-Trump candidates.

“My friend Richard Burr made Lara Trump almost a sure-fire candidate for the Senate seat in North Carolina to replace if she runs,” he said in an interview with Fox News.

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

She did not immediately respond to a request for comment. A senior Republican official, aware of her plans, said the January 6 riot pissed her off at running, but Ms. Trump would decide over the next few months whether to run as part of a coordinated Trump family comeback.

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

“We’re going to take a closer look at each candidate in comparison to some sort of coronation,” said Mark Brody, a member of the Republican National Committee from Union County outside Charlotte.

Doug Heye, a former RNC spokesman who previously worked for Mr. Burr, asked if Ms. Trump was ready to endure the hassle and boredom of running or serving. “A lot of people love speculation and attention, but being a senator is a lot of hard work,” he said.

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

If she runs, the Trump family could be a liability on a battlefield that the former president only gained 1.3 percentage points in 2020 – or it could bring no benefit at all in 2022, depending on the political environment.

“There’s a myth that Trump voters will come out for Trump candidates or family members,” said John Anzalone, a Democratic pollster who has campaigned in the South. “Cult members only appear in full power for the cult leader.”

And Ms. Trump’s candidacy could help increase Democratic turnout, especially among the state’s large black population, and counter the typical decline in most mid-term elections.

But Ms. Trump’s boosters, led by Mr. Graham, hope that she can use the backlash in the party’s grassroots base to catapult her to the top of the field.

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

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

But he said Ms. Trump would be “the favorite” when she runs, adding, “Nobody comes closer.”