I could imagine few better candidates for Clinton, Obama or Edwards to run against than Huckabee. Completely beholden to the Christian Right to the point of evolution denial, less experience than any of the Dems (esp. in foreign policy), no enthusiasm from corporate wing of GOP, no money and as close to re-nominating George Bush as you can get.
Rudy and Romney could possibly pivot to the center, while still using the fear card on immigration and terror to try and scare the public into voting R again. I don't think it will work, but they pose a larger challenge than Huckabee would. Next to Hillary, Obama or Edwards, Huckabee is just outclassed. There's little love for big government conservatism outside of the 24% of dead-enders still supporting President Bush. The Democrats would look like presidents. Huckabee looks like a cross between a Subway spokesman and a televangelist. It would be a recipe for a landslide, with a possibility of winning every state outside of the south. He's like George Bush without the money, or the campaign organization.
Update after jump
UPDATE I understand the populist arguments being set forth as potentially hurting the Democrats if Huckabee becomes the nominee. Huckabee's raising of taxes to support social programs sounds... damn librul. And of course, his aw shucks, religious demeanor in endearing to the guns and God crowd. However, I think it is a mistake to instantly correlate that with the successful Bush and Reagan candidacies.
First of all, times have changed since 2000. In 2000, times were such that a candidate could run on likeability alone because, tragically, the election was seen as something that didn't really matter. The events of the last 7 years have totally changed the equation. Another Bush 2000 compassionate conservatism candidacy would be crushed because of sheer gravity of the issues the nation faces. Running a candidate who is clueless on foreign affairs is electoral suicide for the Republicans, no matter how good his barbecue skills are.
Second of all, Reagan and Bush ran with the most impressive party machinery seen since the New Deal at their backs. They had more money than the Democrats, and had a more united coalition hell bent on victory. None of the Repubs will have that this time, but Huckabee will by far be the worst off in this department. He simply does not have the support of the anti-tax big-business wing that's necessary for fundraising. He will be completely drowned out on the airwaves by whoever is our nominee, including Edwards.
There are some admirable aspects of Huckabee's candidacy. I like that he's realistic when it comes to paying for programs through taxes. I like that he doesn't demonize immigrants. But his extreme social positions will be impossible to cover up.
Personally, I think it's unlikely that he gets the nod. But if he does, his handicaps are higher than Rudy's. Rudy will keep the social conservative base because of his authoritarian pro-war, anti-immigrant bent. He will also have a more potent war chest, and have the party machinery more solidly behind him. Romney would be a better fundraiser than Huck, although I don't know how well his Mormonism will play in keeping social conservatives on board.