You need to understand that us "right-wing" conservatives only make up a part of the GOP base. Libertarians and free-market independents will oppose Rudy too, because he's an authoritarian.
Rudy's nominated = 3rd party
And that will get the same results as the last time it happened, A Clinton in the White house. But , hey we got rid of that Rino George Bush. And look at the great results it begot.