Who will replace Lindsey Graham in the Senate?

Rep. Nancy Mace, R-S.C., and South Carolina Gov. Henry McMaster are among the first two names being floated in what could be a crowded field to fill the seat vacated by Sen. Lindsey Graham, R-S.C., who died suddenly over the weekend.

Graham was seeking reelection at the time of his death and was due to square off against Democrat Annie Andrews in the general election this November, in a race the Cook Political Report with Amy Walter had labeled “Solid R.”

A person familiar with Mace’s thinking, who spoke on condition of anonymity, said she is “strongly considering” running for the seat and would be out with polling on Monday. 

Mace, who has represented South Carolina’s 1st congressional district since 2021, launched a campaign for governor but lost in the Republican primary in June.

“South Carolina lost a giant last night. For more than three decades, Lindsey Graham gave everything he had to this state and this country, from the Air Force to the United States Senate,” Mace wrote on X on Sunday. “We did not always agree, but no one ever questioned his love for South Carolina or the fight he brought to every room he walked into.”

In a subsequent post on X on Sunday, Mace referenced “The Godfather Part III.”

“‘Just when I thought I was out… they pull me back in…'” she posted.

Meanwhile, President Donald Trump, the preeminent kingmaker in Republican politics, said on NBC’s “Meet the Press” Sunday morning that “I have somebody I like” to replace Graham, but declined to name who it is.

“I’m not going to tell you who now because it’s too soon,” the president said.

Trump, however, heaped praise on South Carolina Gov. Henry McMaster, a close ally, during the interview.

“Henry’s been a great governor, you know now he’s termed out, but he’s going to do the right thing,” Trump said. “I think Henry will be fantastic.”

According to South Carolina state law, McMaster will need to hold a special primary election on Aug.11 to replace Graham on the November ballot. The filing period for that primary will open July 21.

McMaster has the authority to appoint a candidate to fill Graham’s current role. Michelle LeClair, McMaster’s press secretary, told CNBC: “At this time, our focus is on honoring Senator Graham’s life and service. Questions regarding the process for filling the vacancy will be addressed by the Governor’s Office when there are updates to share.”

Punchbowl News had reported that Rep. Joe Wilson, R-S.C., is interested in the interim appointment and would run for a full term.

But Wilson, who is running for reelection in South Carolina’s 2nd congressional district, on Sunday appeared to throw cold water on the claim in a post on X.

“I was grateful to speak with President Trump today reminiscing about our mutual friend, Senator Lindsey Graham. I assured him my goal is to remain in the House to keep his two-vote majority for the American people!!!” Wilson posted.

Others could also join the race.

Rep. William Timmons, who is seeking another term representing South Carolina’s 4th congressional district, said in a statement to CNBC that he was “deeply saddened” by Graham’s passing but didn’t rule out a run.

“If and when the time comes to discuss the future, I have always been willing to serve South Carolina wherever I can make the greatest difference,” Timmons said.

Rep. Ralph Norman, another member of South Carolina’s House delegation who fell short in his campaign for governor earlier this year, is also expected to test the waters, multiple outlets reported.

Graham’s replacement potentially could come from outside the halls of Congress. There is speculation that Lt. Gov. Pamela Evette, who earned Trump’s endorsement in her campaign for governor, could enter the fray.

And Politico reported that Treasury Secretary Scott Bessent, a South Carolina native who has kept a home in the state, was fielding calls from people encouraging him to run. Bessent’s spokespeople did not immediately respond to a CNBC request for comment.