Haley Barbour has, presumably, the exact opposite problem than the one that plagues Sarah Palin's presidential ambitions. Barbour certainly plays by the rules; I don't know what he really thinks about issues, but I don't think there are many GOP constituencies that would worry about being locked out of a Barbour White House, or not being able to cut deals with a President Barbour (some Tea Partiers might sense he's not really their type of Republican, but he doesn't have the kinds of difficult past positions to defend, as far as I know, that many in the rest of the field have).
The problem for Barbour, one that has led many liberals to assume that his candidacy is entirely implausible, isn't going to be with insiders; it's with voters. It is true that Barbour starts with very little support, presumably; he's a small-state governor with little national profile. But the big thing is that as a dealmaking former lobbyist, he seems more like a cartoon character than a national politician. He's no John Thune, or even a Mitt Romney; he just doesn't look the part, and his resume matches the look.
This, however, is where the primaries come in. Republican leaders (as always, interpreted very broadly) who either would be very happy with or at least could easily live with Barbour as president may share the suspicion that voters just wouldn't like Haley Barbour very much. The traditional way to test this has been to watch the results of presidential primaries and caucuses. Candidates who intrigue party leaders but seem risky to put before voters -- everyone from John Kennedy in 1960 to Howard Dean in 2004 and Barack Obama in 2008 -- have "proved" their strengths or weaknesses. Now, I'll be the first to agree that Howard Dean's poor showing in Iowa in 2004 didn't really prove anything, but party leaders need to make choices and don't have clearly better information available, so they're likely to overemphasize what they do have. Thus the demise of Dean after Iowa in 2004, and the flight of party leaders towards Obama after Iowa 2008.
I have no idea whether Boss Hogg will be an appealing image to Republican caucus attendees in Iowa next winter, or to Republican primary voters in New Hampshire. If, however, he can survive those two events (that is, at least a respectable third place finish in both); if no clear nominee has emerged; and if the other finalists are unacceptable to major constituencies within the party...well, at that point, he's a pretty logical nominee. How likely is it that all three things would happen? I don't know, but I'd say better than one in twenty, anyway. If you believe that Mitt Romney is certain to collapse either because of health care (which I don't expect) or religion (which I think is possible, but I can't make odds on it), then Barbour's chances are that much higher.
I said a while ago that I thought Barbour, Jim DeMint, and Rick Perry were the three candidates seriously undervalued in Intrade's market. At that point they were at 2%, 1%, and 1%, respectively; today Barbour is up to 5% while the other two round up to 1% and still have made no formal steps toward running. I'll stick with that bet, still. I'm not predicting one of the three will win, but I think they're all plausible, while, say, Newt Gingrich (steady at a bit under 6%) just is not.