Biden
I really don't think many people are sick enough to put in a Democratic President and a Republican Vice President (and vice versa). It would be a disaster and there really isn't a partisan advantage to it.
if McCain won the House balloting (which would be a shocker but if it were to somehow happen) then it'd be silly for the Dems to roll over in the Senate and give the VP to Palin, as McCain may well die in his first term.
I'm sure they would roll over though, assuming the Prez balloting went first and the results were known.
I believe the House would vote first. If it was known that McCain won in the House then of course Lieberman would vote for Palin. Then it's a question of how Hagel votes. If Hagel goes for Palin, we're at a 50-50 tie. Then what the hell happens?
It would be the new Congress. At the very least, there would be M. Warren and an Udall in it.