I think the campaign would have started off with a moderately sized Bush lead in May (maybe 49-35 Bush or so). Then, by the summer, Clinton wouldh have closed the gap to about 45-45. However, by Labor Day, they would be tied, and by election day, Bush would win about 53-47 or 54-46. I think Clinton would have stressed being the Southern candidate more.
I think it would have produced somewhat of an odd map, maybe something like this:
How does Bush win Wisconsin? It's a Dukakis state. It makes no sense for a state to vote for a weak candidate over Bush at a time when he was fairly popular, and then vote for Bush at a time when he was much less popular over a much stronger candidate.
I say Clinton still wins. Most of the support Perot got outside of the mountain west (besides protest votes) was protectionist Democrats.