I'd expect a very odd map:
A military engagement would probably be key to the oil price increase, so Yemen is a more likely choice for conflict here. That said, in either Syria or Yemen the US engagement would be more along the lines of Libya then Iraq given the facts of the situation and the kind of president Obama has been. Yemen makes more sense as it would probably be a conflict closer to oil producing Saudi Arabia and could lead to disruption of trade around the souther tip of the peninsula. This choice inevitably dictates the type of conflict as well. It would mean the US has either opted to strike real terrorist targets in the country since the government is busy with an uprising, or it has taken sides (probably on the side of the people) and is working to disrupt the Yemeni government in some fashion. To get here would likely require a harsh and very bloody crack down that results in thousands and thousands of deaths, and likely tens of thousands more are to follow. Or... the conflict is looking likely to expand into neighboring countries. Perhaps Saudi Arabia has built a coalition to deal with the fire on its doorstep and the US is helping out to keep the conflict from expanding.
If the choice is Syria things are a little more straight forward as it would likely be played as a humanitarian mission only with no "War for Oil" slogans in use. So the Yemen conflict would be a worse situation for the president as it might turn away liberal minded folks from his campaign.
The problem is, Bloomberg may be an indi now, but has a record of being a Republican. The president can hit him on that relentlessly in the campaign. This would do two things. 1. It would keep a vast majority of dems from voting for Bloomberg. If Obama retains the 40-45% floor of the Democratic Party's usual support, he's in good shape in this situation. 2. It would allow less friendly people to still vote against Obama without voting for the obviously loony Cain. This drives down Cain's numbers among swing voters. Cain retains core Republicans however and thus like Obama, isn't doing to shabby.
So then going state by state, one has to look for the places with solid levels of support for the major parties and which areas might be prone to quality, right leaning, third party bids. I'm probably underestimating this effect in Maine, but it would be strong in Minnesota for sure, and NH might be Bloomberg's best state. I think claims that Bloomberg would upset in NJ/NY/CT are overblown. NYC politics is not the same as national politics and NYC people know this.
As for the south, it runs into a clear situation of solid dems and split republicans. Despite racial progress and all that, if some conservative white people who would normally always vote Republican had a chance to vote for a white conservative over two black guys, they'll take that option. I suspect it would be enough to cause a near sweep of the region by the president, the exception being the western south which seems to work a little differently these days compared to the deep south.
The only reason I don't give Obama Texas is the troubled economy and the strength of the Republican party to organize here without relying on racial dog whistles state wide.