I doubt you would see a candidate from the US winning many votes from the rest of the world, for the same reason we'll never see an American pope or UN Secretary General. Political elites in the US would probably end up supporting someone from Western Europe.
I agree it would be difficult for Americans in general, but Obama would be almost uniquely positioned to be able to win.
Although it could be a multi-round system, I'm mostly interested in what a two horse race would look like, whether it emerged "naturally" or via a run-off.