tl;dr: Maybe we get a much more forceful and progressive reigning in of the financial sector.
People like Bloomberg move in strangely opaque circles, so I can imagine him being convinced this is something the people want. I think the more likely thing to happen if Huckabee is the candidate is he meets with Obama, realizes he's working with another moderate, and agrees to stay out. But it's by no means certain that would be the case. Enough disaffected Clintonians exist near his orbit that he might be convinced to just go for it.
While I agree with David T on the fundamentals, badly thought-out political campaigns are there own kind of fundamental truth. So let's say he runs.
First off, Huckabee starts off with a sturdier base than McCain. The special interests are placated and the establishment likely feel they have control over the situation (it's funny, they tend to feel that way no matter what the circumstances). Somewhat higher enthusiasm on the right, softer support towards the center but he was really trying to work that compassionate conservative angle in '08 so he's got some messaging aimed at the moderates at least.
Fundamentals for Obama are the same. His message was broad and pure political gold. If Bloomberg plops in the middle, he can push harder to the middle and still be certain that his left is strong, or push to the left and keep his middle happy with positive messaging. He might lose a few technocratic types and will certainly lose a number of large donors. This could allow him to go harder after the financial sector during the campaign. While maybe not in-line with his inclinations, it's good politics that appeals to the working and middle class whites that Obama has a chance at winning over. (Mostly in suburbs in blue states he's already going to win, but still, pad the numbers.) Otherwise talk over Bloomberg and say what he says but more eloquently and win those news cycles.
Bloomberg makes a small coalition from true moderates, those moderate hawks that loved McCain, and the strangely fervent remnant of Clintonian DLC voters who couldn't reconcile themselves to Obama. And then, you know, a few well-off congressional districts in the northeast probably give him above-average support, and probably some above-average Jewish support.
I'm inclined to say Obama suffers more than Huckabee, just because OTL was an Obama blowout and he's got more votes to lose. But then that was against McCain. In the end I think the Republicans are more enthusiastic about their guy, plus more Republican-leaning voters are voting than IOTL because conservatives who stayed home IOTL are out and moderates who went for McCain are out for Bloomberg. The Democratic majority is maybe a little smaller. Obama maybe loses a couple states he won IOTL- Indiana and Florida come to mind- but he also might make a couple pickups in the likes of Montana and Arizona.
If Obama, unfettered by the need to court the financial sector, takes the opportunity to bash that sector- keeping in mind the financial crisis is around our ears at this point- we could see a much stronger regulation of that industry once he takes office. That could be the biggest effect from this.