NEW YORK -- Since last October, when President Barack Obama visited the set of "The Daily Show," the majority of political guests on the show have been conservatives.

Though he leans left, host Jon Stewart has coaxed plenty of Republicans -- including potential 2012 contenders Tim Pawlenty, Mike Huckabee and Newt Gingrich, Tea Party leader Dick Armey and even longtime punching bags like former Defense Secretary Donald Rumsfeld and former RNC chair Michael Steele -- to appear on his show and engage in lively debate with one of the most well-respected interviewers on television. But a few high-profile conservatives looking to expand their base and move new books keep declining the show's invitations, despite the fact that Stewart is typically gracious with right-wing guests (after his recent appearance, one of the toughest interviews he endured on his book tour, Rumsfeld tweeted: "Just wrapped up one of the most thoughtful interviews of book tour with @thedailyshow").

Glenn Beck, Sarah Palin, Mitt Romney and John McCain -- whose last appearance was in early 2008 -- keep holding out on Stewart, most likely due to a strategic call that there are more minuses than pluses to being a guest, especially the potential to commit a gaffe that is bound to make headlines, say media analysts.

Palin has been invited numerous times by Stewart, most recently on Jan. 18 during an extended mockathon. "Join me -- I would love to have a conversation with you. We'll do it in my studio, your wilderness utopia," Stewart quipped. "You could have Glenn Beck sit next to us or between us. I want him to come on too. He won't do it either. I promise a pleasant, respectful and classy conversation."

Asked for comment, Palin aide and unofficial spokeswoman Rebecca Mansour emailed The Huffington Post, claiming that Palin "doesn't recall being invited on Jon Stewart's show" and that no one at her political action committee, SarahPAC "remembers seeing an invitation," adding that the former governor's Fox News contract precludes her from appearing on other networks without approval.

When it was suggested that perhaps she and the other holdouts were afraid to go on the show, Mansour emphasized: "She is certainly not 'afraid' to go on his or any show. Sometimes she chooses to avoid a show, such as David Letterman's, because she doesn't want to give it a ratings or publicity boost. But afraid? No way."

In a follow-up email, Mansour was more vehement: "She's not afraid of his show. She doesn't think about him all that much. Neither do I. However, I do recall that he's been rather vicious in his coverage of her, so I'm not sure why she would even want to appear on his show to give him a ratings boost. If you continue to imply that she's afraid of appearing on a comedian's satire news show, then you're just plain wrong. She's stared down big oil companies and won. Jon Stewart isn't all that intimidating."

Palin's reluctance is perfectly understandable to Richard Parker, lecturer in public policy at Harvard's Kennedy School. "If I were Sarah Palin and remember what Katie Couric did to me, I can't imagine what Jon Stewart would do to me," he said.

But Parker sees this as more a matter of strategy than fear of Stewart when it comes to conservatives "who are handled with kid gloves in their own environment."

"If I'm a media adviser, what's the upside for me in doing this?" Parker asked. "Palin is problematic on her feet under pressure -- all he needs is one gaffe that he can exploit to make you look like an ignoramus. He does with humor what [MSNBC host] Chris Matthews does to a less effective degree without humor -- he'll nail you and once you're down, he'll keep nailing you."

That apprehension may indicate why only one former member of George W. Bush's cabinet, Secretary of Education Margaret Spellings, appeared on the show during the eight years of Bush's administration. By contrast, during Obama's first two years, at least six cabinet-level secretaries have been guests, plus the head of the Environmental Protection Agency and First Lady Michelle Obama, reported the Washington Post.

Beck and Stewart seem to have a loving relationship, in the sense that the "Daily Show" host loves to make fun of Beck's histrionics and Beck appears to love being hated by Stewart's fans. And they've each had fun making fun of the other's massive rally in Washington.

The Fox News host has become one of Stewart's favorite crowd-pleasing punchlines -- the comedian has performed several elaborate skits in which he dons Beck's signature glasses and apes Beck's hand gestures and tear-laden outbursts in front of chalkboards. In January, Stewart responded to Beck's appearance on "The Today Show," in which Beck defended his violent rhetoric by comparing his shtick to Stewart's comedic antics, by inviting Beck on his program.

"Once again, my brother -- you, my friend, and I ... I would like you to be on our show, by which I mean appear on our show so that you can get some things off your chest," Stewart said. "I'll sweeten the deal, brother-man," he added, holding up a five-chalk holder to tempt the Fox News host known for his extensive use of blackboards to illustrate elaborate conspiracy theories, most recently linking the unrest in the Mideast to the union-led budget protests in Wisconsin.

Beck, who has turned down interview requests from network news programs like "Good Morning America" and "The Early Show" as well as late-night comics like Jay Leno and Jimmy Kimmel, tends to ignore Stewart on his TV show and has been complimentary in interviews. He told New York magazine that Stewart "is very funny, and if I were in his position, I'd be doing a lot of the same things. In fact, a lot of the jokes I've heard before, either from my staff or myself. He takes things out of context (no worse than most of the other mainstream media) and is more interested in being funny than trying to actually understand the key messages in [my] show... Good for him, keep doing what he's doing. People seem to like watching my show as well, and hopefully that continues for both of us for a very long time".

But on his radio show, Beck uses the "Daily Show" host as a convenient foil to his own man-of-the-people persona. His producers occasionally chime in to attack Stewart, and Beck typically responds with a casual disdain. During one show last September, Beck told his listeners that "I am so sick of my own staff going, 'Did you see Jon Stewart last night?" No I didn't see it. I didn't see it. I don't care."

Later, when his producers mentioned David Letterman and Stewart swapping stories about Beck turning down Letterman's invitation and not inviting Stewart on his show, Beck joked with his producers, "I wear those both as a badge of honor." He explained his refusal to have Stewart appear on his show, though Stewart has been a guest several times on fellow Fox News host Bill O'Reilly's program, by deriding Stewart's profession. "This week, let's see. I've had the Holocaust survivor and the historian on as a guest this week," Beck said. "I'm trying to think where the comedian comes in. I mean, I just don't do those interviews."

In January 2010, in the online version of his show's transcript titled "Stewart gets owned, hits Glenn," Beck and his producers lashed out at Stewart for mocking Beck's first interview with Palin and claimed that he was "schooled" by former Bush Justice Department lawyer John Yoo during an interview. On Beck's site, one of his show's segments was headlined: "Should Glenn seek a restraining order on Jon Stewart?" -- adding, "Glenn can take a joke, that's completely fine, but this is just getting creepy." And back in 2009, shortly after Stewart's first impression of Beck, which implied that Beck disregards the facts in his discussion of health care reform, the Fox News host responded defensively that his argument "revolves around facts" and added:

"Did you ever stop to think that maybe Jon Stewart just looks into the camera and doesn't bother trying to make sense of his arguments? I mean, you know, not because he's a comedian but because he's 100% sure his audience wouldn't put a second thought into what he's saying?"

Beck declined comment through a spokesperson.

McCain is an example of a love affair gone bad -- the senator was once Stewart's most frequent guest and he made 13 appearances on the "Daily Show." Their lively debates about McCain's visit to Liberty University and the Iraq War were grounded in mutual respect and they regularly referred to each other as friends. But when the 2008 election grew more heated with his selection of Palin as a running mate, McCain avoided the show and has never returned despite a standing invitation to come back.

McCain's intransigence has gotten so bad that Stewart regularly refers to his former friend -- most recently, out of frustration and for laughs (of course), he said that McCain's "old man crankiness has gone off the charts" before announcing a new mission to annoy the senator and introducing a cranky Puppet John McCain hurling insults at Stewart (calling him a "first-class asshole" and giving him the finger).

McCain spokeswoman Brooke Buchanan did not return five emails or several phone calls for comment.

And Romney, a 2008 presidential contender and likely candidate in 2012, has never appeared on the show. His spokesman, Eric Fehrnstrom, did not return several emails for comment.