I'm sure there will be resistance from conservatives, but I suspect Guiliani will position himself to take it, particularly if Hitlery is the Dem nominee. Guiliani v. Hitlery ought to be a cinch for Guiliani.
I'm not convinced that Cheney will serve out 4 years, given his health. Whoever Bush nominates to take his place will have the inside track. Could very easily be Guiliani. Guiliani worked like a dog to get Bush re-elected.
If Cheney does step down, it has to be someone from the Senate to take over.. That person could be Frist...
If this happens, my guess is he'll pick Tom Ridge as VP, then pick Giuliani to replace Ridge as homeland security director. That rewards Giuliani for his work, and puts him in a position appropriate for his experience.
Bush clearly likes Ridge given the confidence he placed in him. That job was high profile - the first director of a new agency whose founding purpose was to stop terror attacks. If they were incompetent it would have had serious consequences.
Bush convinced Ridge to leave his governorship to take a politically risky job. If a terrorist attack hits us at some point, Ridge's career is likely finished. That's more reason for me to think he's in line to be rewarded.
The public would accept his qualifications. He was a successful governor, then succeeded as homeland security director. That makes him very credible as a national security candidate. The Congress would have a hard time rejecting him, and the voters would elect him in '08.