State Sen. Lee Bright (R) has gotten national attention for backing "extremely conservative legislation" according to The New York Times.
He's aligned himself closely with former Rep. Ron Paul (R) and supported him when the Texan ran for president. Bright has also been supportive of Sen. Ted Cruz's (R-TX) push to continue to fund the government only if it meant defunding Obamacare. After the shutdown ended, Bright said Republicans may have lost but at least conservatives now "have a list for voters to decide if they're gong to tolerate that kind of behavior."
In 2012, Bright supported South Carolina Gov. Nikki Haley's (R) veto of $450,000 for rape crisis centers in the state. In return, Haley campaigned for Bright, helping him fend off a primary challenger.
Attorney and businessman Richard Cash ran for Congress in 2010 and was defeated against now-Rep. Jeff Duncan (R-SC) in a runoff. This time around, Cash, an early supporter of Rick Santorum's presidential candidacy, has positioned himself as a strong social conservative, offering regular praise for tea party favorites like Cruz, Rand Paul (R-KY), and Mike Lee (R-UT).
"We're moving from a Judeo-Christian heritage to a secular culture," Cash said according to CNN. "And we're moving from a constitutional republic with a limited government and the rule of law to a big government with centralized power and the rule of men, where whoever's in charge forces their power on the public."
On Graham, Cash has described the senator as a "moderate" in contrast to Sen. Tim Scott (R-SC) who, Cash says, is a conservative.
Bill Connor jumped into the race last week, making him the fourth (and most recent) Republican to challenge Graham. Unlike the rest of the field, Connor has run a statewide race before. He lost the 2010 Republican primary for lieutenant governor by a slim margin in a runoff against Ken Ard. Both Connor and Ard campaigned on tax reform and bringing more business to the state. Connor, a graduate of The Citadel, has described himself as a political outsider, according to The State newspaper.
"I am the only candidate in the race not tainted with elected or appointed office," Connor said during his lieutenant gubernatorial bid, according to The State. "Right now, there is a feeling in the Republican Party that, for the last eight years, they have blown it and have not held to their core, conservative principles."
Nancy Mace is a public affairs consultant and the first female graduate of The Citadel Corps of Cadets in Charleston, S.C. She's been one of the more visible challengers in the field, starting her candidacy off with appearances in local media and some hype. She's also argued that it's "meaningless" to elect Republicans if they aren't "strong conservative leaders," rhetoric that matches the arguments of prominent outside groups like the Senate Conservatives Fund and Club For Growth. But Mace hasn't been able to gain the endorsements of those groups.
She's also suffered from some bad press. Redstate.com editor-in-chief Erick Erickson wrote that he would not support Mace, largely citing her ties to South Carolina blogger Will Folks. Mace also got some negative attention when her twitter account retweeted a post calling Graham a "Nancy Boy."