No way the conservative base would turn out for Giuliani. And I think the Obama campaign would work overtime to burn into their brains that infamous photo of Rudy in drag.
Crime alone wouldn't make a difference. We aren't in the 80's and Obama was no Dukakis.
His 9/11 schtick had already become a staple of late night comedians, and with Biden on the Democratic ticket it would be even moreso.
Finally, it wasn't so much his inept campaign that doomed Giulian, as much the fact that wherever he campaigned, his poll numbers tanked. The more the voters saw the guy, the less they liked him.
With Obama the exact opposite happened. You do the math.
