COLUMBIA, S.C. (AP) -- The resignation of U.S. Sen. Jim DeMint gives Gov. Nikki Haley sole authority to choose South Carolina's next senator, and the only indication she made Thursday is that it won't be her.
Speculation abounds over who she might pick to fill the seat through 2014, when voters will choose someone to serve the remaining two years of DeMint's term. The name game began as soon as DeMint announced his resignation, effective Jan. 1, to become president of the Heritage Foundation, a conservative think tank.
Names tossed out as possibilities include the state's four congressmen recently re-elected to their second term.
Haley could make history by appointing Rep. Tim Scott. The former Charleston County Council chairman would become South Carolina's first black U.S. senator ever and the chamber's first black Republican from the South since Reconstruction.
Scott, a former state House member, did not immediately respond to messages Thursday from The Associated Press.
But Rep. Trey Gowdy, a former prosecutor from Spartanburg, said Scott would be his top choice. He noted that Scott has already been named to Ways and Means, the House's tax-writing committee.
"If she asked my opinion, I would tell her there are two members of the delegation I wished she would consider, and I'm not one of them," he said. Gowdy said the other would be Rep. Mick Mulvaney.
Mulvaney, former state representative and senator from Indian Land, said he was contemplating running to replace DeMint in 2016 anyway. DeMint had said he wouldn't seek a third term, but his resignation stunned even his congressional colleagues.
"Certainly, it was something we'd looked at," Mulvaney said about 2016.
State Sen. Tom Davis, R-Beaufort, believes Mulvaney would be the best match for replacing DeMint, considered an ideological godfather of the tea party movement. Davis likened DeMint's stunning announcement amid Congress' debate over the so-called fiscal cliff to a general leaving in the midst of battle.
"We're struggling right now for the soul of the Republican party. There's a very real ideological battle going on," he said. Haley needs to appoint someone who "truly believes in individual liberty and smaller government."
Davis, who has been mentioned as a possible challenger to U.S. Sen. Lindsey Graham in 2014, said he told the governor's office he's not interested in the appointment. He advocates Mulvaney.
"I've seen him withstand the pressure of Washington, D.C. I've seen him take unpopular stands. It takes someone like that to continue this fight," Davis said.
State law gives Haley no deadline, though she said in a radio interview she won't drag out a decision.
If Haley chooses a U.S. House member, voters would then fill that seat in a special election. State law treats filling vacancies for U.S. House and Senate seats differently.
The names floated Thursday also include former Attorney General Henry McMaster, once considered the front-runner for governor until Haley surged late in the 2010 four-way gubernatorial primary. McMaster has been a strong ally since. Haley recently named him co-chairman of a committee to study ethics reform in the state.
Another possibility is former U.S. Ambassador to Canada David Wilkins, appointed ambassador by President Bush in 2005. Before that, the Greenville Republican served 25 years in the state House, 11 of them as speaker.
Wilkins said he had received no phone call from the governor's office and doesn't expect one.
DeMint's spokesman said the senator is not getting involved in Haley's choice.
"Sen. DeMint has no favorites as our state has a deep bench of conservatives," Wesley Denton said. "This is Gov. Haley's decision alone and he trusts her to make a great choice."
Haley could arrange for herself to step into DeMint's seat. But she appeared to rule that out.
"I will not be appointing myself. That's not even an option," Haley told WORD-FM.
Under state law, Haley would have to resign as governor. The appointment would then have to come from Lt. Gov. Glenn McConnell, after he assumed the governorship.
The last time a governor arranged to send himself to the U.S. Senate, he didn't stay very long. Former Gov. Donald Russell became senator in 1965 after the death of Sen. Olin Johnston. Voters booted him out a year later.