Is South Carolina big enough for Lindsey Graham and Jim DeMint? They are hardly friends and they clearly disagree about the direction of the Republican Party.

On Wednesday, South Carolina’s two senators, Lindsey Graham and Jim DeMint will get together high above Washington, D.C. They will take in views of the Mall and the Capitol from the rooftop of a Washington law firm, joining other Republicans from their state’s congressional delegation for a fundraiser to honor Republican gubernatorial candidate Nikki Haley in style.

In this fractious campaign year, the occasion is a rare one. When was the last time Graham and DeMint had the same view of anything?

There’s a civil war brewing in the Republican Party—the most recent battlefield was the GOP Senate primary in Delaware where Christine O’Donnell, the Tea Party candidate endorsed by DeMint, triumphed over Rep. Mike Castle, who was backed by Graham. And nowhere is the battle being fought in closer quarters than in the South Carolina Senate delegation where conservative DeMint, driving to purify the party, and Graham, often an island of moderation, exist in an uneasy peace.

With the primary victory of O’Donnell, DeMint put the final touches on a remarkable year, where he’s moved from full-time conservative irritant to a big-time player in Republican politics, providing inspiration and money for a slate of right-wing Senate candidates. (Junior DeMints, as they are known in some quarters). DeMint’s vision, however, of a Republican Party cut to its conservative core, is the opposite of Graham’s.

While not completely immune to the rightward pull of his party, Graham has dared stick his nose outside the Republican tent. For a moment, he was an evangelist for climate change legislation, and was willing to reach across the aisle on immigration reform. Graham also tried to work with the White House on its plan to close Guantanamo Bay. And he has supported Obama’s Supreme Court nominees, Sonia Sotomayor and Elena Kagan. DeMint, for his part, hasn’t cottoned to any of those deviations from the party line.

The Republican Senate primaries are a good measure of the distance between Graham and DeMint. In five races, Graham and DeMint found themselves endorsing different candidates. In Florida, DeMint backed Marco Rubio while Graham stood behind Gov. Charlie Crist—at least while he was still a Republican. In Colorado, DeMint sided with Ken Buck while Graham gave money to Jane Norton, who has plenty of ties to Graham buddy John McCain. In California and Indiana, Graham and DeMint found themselves backing different horses. And then there was Delaware and O’Donnell. For those keeping score, that’s three wins for DeMint, and two for Graham.

“I don’t think they have any animosity, but I don’t think they have any abiding friendship.”

“I’d rather have 40 Marco Rubios than 60 Arlen Specters,” DeMint told ABC News last week about his desire for a leaner, more conservative GOP.

“I'm a coalition guy,” Graham told reporters Monday. “I believe there needs to be a place in the Republican Party for the Tea Party. They bring a lot of energy. But there has to be a coalition. A social moderate and a fiscal conservative--you're welcome in my party.”

Asked whether DeMint is bad for the Republican Party, Graham said, “Anybody who's pursuing with passion what they believe…is doing the country a service. And Jim I think is doing what he's doing passionately and honorably.”

In South Carolina, many point to their personal relationship as the reason why they have managed to keep major disagreements out of view.

“The personal relationship they have trumps the differences and approaches they take,” says Merle Black, an expert on Southern politics at Emory University.

But others say that privately, Graham and DeMint aren’t so quite so convivial.

“They don’t socialize,” says David Woodard, a political scientist at Clemson University who co-authored a book with DeMint in 2008 and managed Graham’s campaign for Congress in 1994. “I don’t think they have any animosity, but I don’t think they have any abiding friendship.” He offers this by way of explanation: “Lindsey is a bachelor. Jim is married with children.”

Although DeMint’s four children are grown and married, it’s true their backgrounds and family situations differ. Graham is a 55-year-old former JAG lawyer, the Senate’s most famous single man. DeMint, four years his senior, is a family man who ran his own market research firm before running for office.

In Washington, they cut very different figures. Graham relishes being at the table, and in becoming John McCain’s wingman, Graham quickly picked up on the way things get done in the Senate. DeMint is far less clubbable. His full-throated opposition to earmarks rubbed even his own party the wrong way, and his comments that health care would be Obama’s “Waterloo” sent the party in retreat.

But in some ways, Graham and DeMint offer the perfect coupling. For conservative principles, South Carolinians can look to DeMint. For pork, Graham’s their man. Graham ranks near the bottom in terms of earmark acquisition in the Senate, but he can bring home federal dollars, like the $21 million he secured for an Air Force base this year.

The question for Graham is whether DeMint will cause him trouble in the future—Graham is not up for reelection until 2014. While DeMint has said nothing to cast aspersions on Graham’s record, in a way, he’s already done plenty of harm. As voters at home know, few leaders have been as prominent in routing moderates like Graham out of the party.

“Name me another senator that has been more outspoken in calling out Republicans and Democrats alike,” says Greenville County Republican Party Chairman Patrick Haddon. “I can’t think of another U.S. senator that has been out there and done a better job of endorsing true Republican candidates.”

While no one expects DeMint to support a primary challenger against Graham, when the unreserved senator turns mute, it can still speak volumes. Just ask Bob Inglis, the South Carolina congressman, who was shellacked by primary challenger Trey Gowdy in June. DeMint who used to hold Inglis’ fourth district seat stayed silent during the campaign. It’s possible he could perform a similar disappearing act when Graham’s up for reelection

“Is that silence deafening? It could be,” says David Woodard, the DeMint intimate and former Graham campaign manager.

Graham knows that he needs to make amends with the DeMint wing of the party. He’s gone from insulting Tea Party groups (“It will die out,” Graham has said of the movement”) to courting them. This month, Graham met with a Tea Party organization in Charleston.

Looking at the future ideological contest between Graham and DeMint inside the South Carolina GOP, Haddon says, “I really believe there will be a lot of tension in the party. People saying, ‘We’ve had enough. We’re done.’ It will be interesting.”

Samuel P. Jacobs is a staff reporter at The Daily Beast. He has also written for The Boston Globe, The New York Observer, and The New Republic Online.

Benjamin Sarlin contributed to the reporting to this story.