Updated

South Carolina Sen. Jim DeMint's abrupt resignation has opened up a succession battle in the Palmetto State, with some conservatives openly advocating for Gov. Nikki Haley to appoint Rep. Tim Scott -- who if chosen would be the first black Republican senator in decades.

Sources familiar with the situation told Fox News on Friday that Haley, who holds the power to install a successor until a 2014 special election, is leaning toward choosing a caretaker senator who would not run in two years. They say she's thinking of David Wilkins, former South Carolina House speaker and ex-U.S. ambassador to Canada, for that job.

However, some have been pushing for Haley to instead tap Scott, who would be more than a placeholder. The cheerleading began almost immediately after DeMint announced Thursday he would be leaving the Senate in January to head the conservative Heritage Foundation.

"Gov. Nikki Haley now has the ability to give the US Senate its only black Senator -- a conservative from South Carolina named Tim Scott," conservative blogger Erick Erickson tweeted.

A petition has also started to circulate calling Scott a "staunch conservative that will continue Senator Jim DeMint's efforts to further our cause."

The Tea Party-tied Scott is well-liked among conservatives, but his selection would also carry some historic significance. If picked, he would be the first black Republican senator from the South since Reconstruction, and the only black U.S. senator in the next Congress. The last black Republican senator was Edward Brooke, who represented Massachusetts until the late '70s. South Carolina is also the state that sent segregationist Strom Thurmond to the Senate.

A report in The Hill newspaper claimed that, according to unnamed sources, DeMint has made clear he wants Scott to succeed him in the Senate.

DeMint's South Carolina colleague Sen. Lindsey Graham, without getting into names, told Fox News Radio that there have been discussions about a successor, and that he and DeMint are on "the same sheet of music."

The decision, though, rests with Haley. Asked Thursday whether he'd heard from the South Carolina governor, Scott told Fox News he had not.

"The governor's going to do what the governor's going to do," Scott said, declining to say whether he's interested in the job.

Whoever is selected who have to run in 2014, and again in 2016 for a full six-year term -- barring a prior agreement not to run in 2014, as would likely be the case with a candidate like Wilkins, who is also friends with Haley. Another possibility could be former South Carolina Attorney General Henry McMaster, who at first ran against Haley in a primary and then helped her in the runoff.

In terms of a more permanent pick, there's always the chance Haley could choose herself -- or one of the other members of the South Carolina congressional delegation which includes Reps. Jeff Duncan, Trey Gowdy and Joe Wilson.

Van Hipp, former chairman of the South Carolina GOP, said there's yet another scenario that could "get legs" in the coming days and weeks. He said Haley could opt to install the popular state treasurer, Curtis Loftis, and in doing so please fiscal conservatives while removing a possible primary opponent for her seat.

"There's a lot of intrigue in South Carolina," Hipp told FoxNews.com.

Fox News' Chad Pergram and FoxNews.com's Judson Berger contributed to this report.