A hacking episode resulted in the theft of South Carolina taxpayers' personal information and a public relations problem for Gov. Nikki Haley, also up for re-election this year. Graham advised her on the situation, and now she has better poll numbers than he does.
Not long ago, Graham looked vulnerable to a primary challenge from conservatives offended by his bipartisan dealmaking and votes for President Barack Obama's Supreme Court nominees. Tea party challenges ousted GOP incumbents in the past two elections, and, some believe, prevented the party from regaining the Senate.
But Graham's power and shrewdness, not to mention the intimidating $7 million treasury, have positioned him to cruise to the nomination and likely re-election in November. He's benefited from the support of establishment Republicans and allied groups such as the U.S. Chamber of Commerce focused on gaining the six seats the GOP needs to retake the Senate.
Two top potential rivals let people know early on they were out.
State Sen. Tom Davis, an aide to former Gov. Mark Sanford, predicted before the Republican convention in 2012 that South Carolina voters would oust Graham. But Davis said he could do more for his libertarian-leaning causes in the state Senate, and that to run against Graham, he would need to raise a lot of money.
There was a movement to draft Mulvaney, but he demurred, saying he doesn't enter races he can't win.
Graham still attracts criticism from libertarian Republicans and tea partyers. But polls show none of his challenges tops 10 percent support with eight weeks to go before the primary.
"While he is definitely a public whipping boy for one subsegment of the party, a lot of people in power recognize how influential he is," said Scott Huffmon, a political science professor at Winthrop University.
Graham has largely been unchallenged during his career. He positioned himself to replace retiring Sen. Strom Thurmond so efficiently that he faced no opposition in the 2002 primary. He breezed to re-election in 2008 after spending his first six years working with a Republican president and before the rise of the tea party.
But in his second term, Graham has worked with Democrats on immigration and praised Hillary Rodham Clinton's work as secretary of state, although he has distanced himself from Clinton over the attack on the diplomatic outpost in Benghazi, Libya, that left four Americans dead.
On Obama's nominees to the high court, Graham says he believes the advice and consent power given to senators in the Constitution isn't an ideological test, but a measure of fitness for the office.
Graham's re-election is far from a sure thing.
A Winthrop University poll found his approval rating among registered voters in South Carolina at 40 percent, compared with 49 percent for Haley.
Graham does have six GOP opponents. Three are lawyers, including one who's also a minister. There's one of the most conservative state senators, a man who supported his family with a fleet of ice cream trucks, and the first woman to graduate from the Citadel.
Each is outspoken and keeping alive the idea that Graham is not sufficiently conservative.
They have allies among the half-dozen or so of the state's 46 county Republican parties that have passed resolutions chastising Graham during his second term.
One is Pickens County Republican Party. Chairman Phillip Bowers, says the challengers, at the least, have grabbed Graham's attention.
"Incumbency is so strong, and the money — if you add those two together, I will be very surprised if Senator Graham does not win," Bowers said.
Graham must win a majority of votes in the primary to avoid a runoff. In a seven-way race, that may be difficult. But South Carolina's primary is open, meaning that independents and even some Democrats may vote for the more moderate Graham in the Republican race.
Whenever he isn't in Washington, Graham is campaigning.
The money the senator has amassed for his race means he can run ads almost daily, host free barbecues and ice cream socials and organize the more than 5,000 precinct captains that he claims into a massive get-out-the-vote effort.
Graham's campaign leaves little doubt that the lawmaker, who while in the U.S. House helped with President Bill Clinton's impeachment, is still a conservative. One ad harshly criticizes President Barack Obama's heath care law and promotes Graham's bill to allow states to opt out of "Obamacare." His campaign speech includes a promise to get to the bottom of the attack in Benghazi.
But Graham said what differentiates him from his opponents is that he wants to return to the Senate to improve the country, not just advance the Republican agenda.
"Some want to win this election just to get back power," Graham said. "But the goal should be to win the election with a purpose."
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