It would be interesting to see a President who's a complete dick and doesn't try to hide it at all. I could see something like this happening if the country gets even more polarized than it is OTL, both candidates run dirty, sneering campaigns, and Rove wins by a hair. How to get to that point- I do not know. A Gore victory in 2000 followed by a deep recession?
But how does that get Karl Rove into the Oval Office and the behind the President's desk? A person who is a complete prick and doesn't try to hide it isn't going to be elected President.