Three Republicans have announced bids to unseat Graham: Nancy Mace, a marketing and public relations consultant who was the first female graduate of The Citadel, the Charleston military college; Richard Cash, a onetime anti-abortion activist and former congressional candidate who owns a fleet of ice cream trucks; and state Sen. Lee Bright, a brash conservative who backed libertarian-leaning presidential candidate Ron Paul in his race for the White House.
A fourth candidate, attorney and Army veteran Bill Connor, may join the fray in the coming weeks.
What they have in common is a belief that Graham, who made term limits a centerpiece of his first campaign for Congress in 1994, has been in Washington too long and is too willing to compromise with Democrats on banner issues. His steadfast support for the National Security Agency's surveillance program is particularly upsetting to the state's emboldened libertarian movement, which all of Graham's foes are courting.
"I don't think he is focused on our liberties as much as he is Obama's agenda," Bright said. "You would think as a conservative he would be fighting for the Bill of Rights, trying to protect our way of life. And he is not doing that. He is trying to be the chief negotiator on whatever the deal is."
Bright's small-government disposition and his ties to the Ron Paul wing of the GOP have made him a grassroots favorite in his Greenville-area senate district. But Graham allies have been calling attention to his habit of making over-the-top statements.
On the day he joined the race, Bright labeled Graham, who had traveled on a diplomatic mission this summer to Egypt, "an organizer for the Muslim Brotherhood" -- a criticism he applied to Obama this week.
"I think that Obama is very sympathetic to the Muslim Brotherhood," Bright told CNN. "I think he has got certain embedded hostilities to the American way of life, and he sees them as a group that has been disenfranchised by the leadership of those countries. He is more in line with Muslim extremists than he is with Muslims. He seems to identify with their cause. I don't know if he is a Muslim extremist. But I don't know what his faith is. He professes to be a Christian, so I take him at his word."
The mild-mannered Cash, who came out of nowhere in 2010 to win a Republican primary in the state's 3rd Congressional District before losing a runoff to Rep. Jeff Duncan, is thought to be a sleeper in the race because of his roots in the anti-abortion movement and his quiet relationship with a network of home-school parents in the conservative Upstate.
An early supporter of Rick Santorum during the 2012 presidential race, Cash, who has the kindly look of a pediatric dentist, frames himself as a defender of "Christianity, capitalism, and the Constitution."
Graham backers seem comfortable with the idea of a runoff against Cash or Bright, neither of whom has demonstrated great fundraising prowess or an ability to appeal to Republicans outside the hard-line conservative base.
Woman opponent could complicate things for Graham
The candidate being watched with most interest by Graham-world is Mace. Despite being just 35 years old and having few detailed policy positions other than a list of conservative platitudes on her website, Mace, a mother hailing from a decorated military family in Charleston, has the most intriguing profile of the bunch.
A serious challenge from a female opponent could complicate matters for Graham if he is forced to go negative in the campaign, said Barry Wynn, a leading Republican fundraiser in Greenville.
"South Carolina voters have historically liked incumbents but will not tolerate attacks on women candidates," Wynn said, pointing to Gov. Haley's GOP primary battle in 2010, when a volley of attacks from her male opponents only drove her poll numbers higher.
It's not hard to imagine the fraught nature of running against a woman in South Carolina. In one conversation this week, a senior Republican in the state, a man, recalled an appearance by Mace at a recent GOP event and described her outfit as "not very becoming."
Looming over the race, albeit from his highly paid perch at the Heritage Foundation in Washington, is former Sen. Jim DeMint, the guiding light of limited-government conservatism for many Republicans here. DeMint and Graham often differed wildly on a number of national issues and they are not close friends, but the two have mostly enjoyed a political truce back home for almost a decade.
DeMint has given no indication that he intends to involve himself in the primary, nor do his protégés seem willing to join the fight to unseat Graham.
"I am going to try to let South Carolina determine who they want for their senator at this time," said Kentucky Sen. Rand Paul, who has sparred with Graham over national security issues and civil liberties in the Senate. "It will be unlikely I will be involved. I haven't completely closed the door."
Even the whiff of involvement by DeMint rankles Graham allies.
Republican professionals were taken aback last week when the Senate Conservatives Fund, a political action committee formed by DeMint, unleashed a radio ad accusing Graham of not doing enough to stop the implementation of Obama's health care reform law.
After the radio ad surfaced, Wesley Donehue, a veteran of DeMint's 2004 Senate campaign, took to Facebook to post a television ad from that race in which Graham appeared, defending DeMint after he was coming under withering attack from his Democratic opponent over a controversial tax proposal. DeMint's internal poll numbers were cratering, Donehue said, "and Lindsey stepped up and stopped the bleeding."
"That would have been a much different race if Lindsey hadn't got involved," Donehue said.
What Graham's opponents need most is money, to boost their profiles among the roughly 400,000 Republicans who are expected to vote in the primary and to keep up with Graham's professional organization.
All three of Graham's announced opponents have traveled to Washington to meet with the Club For Growth, a conservative organization eager to topple Graham that often takes sides in Republican primaries, but the group is staking out a wait-and-see approach to this race.
In the meantime, Mace has picked up the support of a well-connected DeMint donor in Greenville, Bill Lowndes, the chairman and CEO of Tindall Corporation. Others in DeMint's network of financial supporters also are keeping an eye on Mace should she become viable.