Back in April, when the debate over torture was roaring, Jon Stewart invited Cliff May, a national-security hawk and former spokesman for the Republican Party, to come on The Daily Show and defend waterboarding. May was hesitant. He thought Stewart would paint him as a crazy extremist. The audience would jeer. It would be a disaster. “I was apprehensive about going on, even though I’ve been on TV for a dozen years,” says May. “A lot of my friends told me: ‘Don’t do it. You’re meat going into the sausage factory.’”

But May had a change of heart after soliciting advice from his friend Bill Kristol, editor of the Weekly Standard. “Kristol told me: ‘You’ll be pleasantly surprised. He doesn’t take cheap shots. Jon is smart. You’ll do just fine.’” Kristol proved to be right. Stewart’s interview of May — a crackling, lengthy debate about where to draw the line between freedom and security — produced one of the most clarifying discussions about torture on television. “Literally, this is the best conversation I’ve had on this subject anywhere,” May told Stewart.

“There is genuine intellectual curiosity,” May told New York. “He’s a staunch liberal, but he’s a thoughtful liberal, and I respect that.” May isn’t the only conservative gushing about Stewart. While the movement professes a disdain for the “liberal media elite,” it has made an exception for the true-blue 46-year-old comedian. “He always gives you a chance to answer, which some people don’t do,” says John Bolton, President Bush’s ambassador to the United Nations and a Fox News contributor, who went on the show last month. “He’s got his perspective, but he’s been fair.” Says Bolton: “In general, a lot of the media, especially on the left, has lost interest in debate and analysis. It has been much more ad hominem. Stewart fundamentally wants to talk about the issues. That’s what I want to do.”

What’s more, Stewart seems to like hosting conservatives (Comedy Central did not reply to requests for comment). In recent weeks, Mike Huckabee, Newt Gingrich, and Bill Kristol have stopped by. Since the beginning of the Obama administration, Stewart has interviewed more conservative pundits than liberal ones. (Remember when fans fretted he’d have trouble finding ways to be funny under the new president?) It may be because it’s simply easier to tangle with an ideological adversary than to needle a compatriot. A clash of ideas is always more entertaining than an echo chamber. And, for a liberal wit like Stewart, it’s easier to stake out a clear position when facing off against a direct opponent. When he’s interviewing a liberal politician or pundit, he comes from a weaker position. His offensive instincts are blurred — notwithstanding his on-air indictment of Jim Cramer — and occasionally he fawns.

Take his interview last month with House Financial Services Committee chair Barney Frank. “It seems like it’s disappeared,” Stewart said of the stimulus money. Frank dodged the attack by insisting that Democrats had made the economic crisis “less bad than it used to be.” Stewart toggled to another point, that Democrats had revised the recovery timetable. Frank claimed his intervention prevented a deeper hole. Frank wasn’t really answering the questions. The conversation felt unsatisfying.

Conservatives like Stewart because he’s providing them a platform to reach an audience that usually tunes them out. And they often find that Stewart takes them more seriously than right-wing political hosts, who are often just using them to validate their broad positions, do. Stewart will poke fun, but he offers a good-faith debate on powder kegs — torture, abortion, nuclear weapons, health care — that explode on other networks. “Shepard Smith did the same discussion [on torture],” says May. “He kept yelling me at me: ‘This is where I get off the bus! Not in my name!’ He wasn’t arguing with me. It was just assertions and anger. That’s not what Jon deals in.”

To be sure, Stewart wants to outsmart and discombobulate his conservative guests. He loves catching them in inconsistencies. “I feel like you just trapped me,” a grinning Kristol told Stewart, after Kristol conceded that the government provides “first-rate” health care to American soldiers. “I just want to get this on the record,” said Stewart. “You just said … the government can run a first-class health-care system.” (Asked about Stewart, Kristol e-mailed back: “I enjoy being on the show, don’t mind serving as his punching bag, and am happy to do my little bit to broaden his horizons.”) But conservatives respect the rules of engagement. They’re trying to trip up Stewart just the same. Says May: “As soon as we finished, he leaned forward and said to me, ‘I can’t believe you got me to say that Harry Truman was a war criminal.’” (Stewart later recanted.)

“Maybe he’s discovered that interesting discussion attracts viewers,” suggested Bolton. But it’s more than that. At the end of the day, the spirited debate on The Daily Show doesn’t leave people feeling queasy or upset — and that includes the guests with whom Stewart spars.