Now a real chess move would be Cheney-Rice 2008. Let the Dems carp over the health issue...yes indeedy, what a disaster....
I can tell you right now that Rice as a Presidential candidate is a non-starter, she lacks the experience and 'gravitas' and would be quick political roadkill. The idea that she would be better than tested politicians to run against Hillary is imho absurd. She needs at least one vetting in an election cycle to consider that ...
OTOH, Cheney-Rice is definitely an interesting combination.
Attempts by Dems to attack Rice as inexperienced, as they tried with Quayle, will backfire.