I observed that if this conversation about how to resolve tough issues were taking place in 2006, I would likely be having it not with Graham but with his friend and legislative mentor, John McCain. “Totally agree,” he responded. “I mean, I was the wingman, O.K.?” But, he acknowledged, things are different now: “John’s got a primary. He’s got to focus on getting re-elected. I don’t want my friend to get beat.”

Image LOYALISTS Graham with John McCain during the 2008 campaign. Once McCain's legislative “wingman,” Graham has become the Republican most likely to try to hammer out a deal. Credit... Chip Somodevilla/Getty Images

I asked whether he was giving McCain a pass on anything risky this year.

“Yeah,” he said. Graham added that he was thinking about a question I recently asked him: would he be so out there, in a bipartisan way, if he were facing re-election this year rather than four years from now? “The answer’s probably no.” Then, as a point of pride, Graham could not resist observing that he had remained committed to immigration reform, which would include some form of a path to citizenship for those illegally in the country, during his previous (admittedly easy) re-election quest. “So I can go to these guys” — meaning, Republicans up for re-election this year — “and say: ‘Listen, I know you’re in the cycle, but so was I. I’m still here.’ ”

McCain was one of “these guys” who was ignoring Graham’s advice. Though Graham did not explicitly say so, he clearly seemed disappointed in his friend’s election-year drift to the right. He did, however, point out a bright side: McCain’s protégé now had an opportunity to show off his own legislative chops. And when it came to shaping the debate, Graham said: “I think I do that better than John. You know, he’s always been a romantic. He’s got to be fighting the bad guys. I’ve never been a Luke Skywalker. I’m a much more calculating guy than that. I understand that you just don’t charge into these things based on some moral belief that you’re right and the other guy’s wrong. I believe that you lay the groundwork before you get involved in these fights.”

It plainly delights Graham to be where the action is — and to let people know it. Yet he seems, for someone so savvy and influential, to lack even the most remedial measure of sophistication. His culinary weaknesses tend toward Chick-fil-A, except when dieting, and sweetish alcoholic beverages like Baileys liqueur and (during our recent dinner) almond schnapps. The row house on Capitol Hill that Graham purchased in 1998 is sparsely adorned, says a friend, “with early college-reject furniture” that was in fact left behind by the previous owner. It took months for Graham to realize that someone had stolen a TV of his, since it was in his kitchen, which he never uses. Bachelorhood would appear to have chosen Lindsey Graham, rather than the other way around — though a former adviser once told me that during Graham’s early Congressional races, stricken-hearted women would show up to the campaign office bearing newly purchased ties and dress shirts for the candidate to wear.

The hyperlinked world leaves Graham utterly at sea. He has never owned a BlackBerry or an iPhone. His staff maintains a Facebook page and posts on Twitter on his behalf, but without Graham’s supervision. The one strand of modern science that rivets Lindsey Graham is the public-opinion poll. Since his first Congressional race in 1994, Graham has employed the services of the South Carolina political consultant Richard Quinn. Quinn’s surveys now find Graham’s approval rating among Republicans at 64, which is 13 points lower than South Carolina’s far more conservative junior senator, Jim DeMint, but still quite high given Graham’s periodic defections from the conservative movement. When Graham takes on an issue, his seemingly off-the-cuff musings reflect his knowledge of Quinn’s data.

Graham revealed his strategic reliance on public opinion over dinner when he brought up the subject of the Guantánamo Bay prison, a post-9/11 legacy of the Bush administration. Gen. David Petraeus convinced the senator that the prison had become an effective recruiting tool for terrorist organizations and therefore must be closed. But, Graham told me: “Eighty-eight percent of the Republican primary voters, when asked ‘Should you close Guantánamo Bay?’ in the poll we took, said no. Now, when you ask, ‘If military commanders said it would be in our national-security interest to close it, and you could do it safely,’ that gets you about 40 percent.” He added: “I believe that if I can get a legal system in place that will convince people that we’re not going to let these people roam loose in the United States, and that we will treat them as military threats, not common criminals — and if the military will stand by me in that process, and if I can get some Bush people saying, ‘This is the right thing to do,’ we can win the day. And I can turn the polling around to at least 50-50. And five years from now when we’ll be in a new stage of the war, this will be an enormous benefit.”

The senator permitted himself a sip of almond schnapps. “Reason always prevails,” he drawled, “if you can market it right.”