The VP's VP

It's January 20, 2009. [John McCain/Barack Obama] is being sworn is as president. Some guy who's spent his whole life talking about how [white people/black people] are ruining this country grabs his [Assault rifle/Sawed-off shotgun] and kills the president. [Sarah Palin/Joe Biden] is sworn in.

Now, it will matter in one case more than in the other but either way it's still relevant: how does a new VP get chosen? I emailed the guy at electoral-vote.com because he knows lots of stuff like this and talks about it all the time.

Chris
If Obama or McCain die in office, how would Biden/Palin then choose their new VP?

The Votemaster
Biden: by consulting with the Senate, cabinet and others
Palin: by asking the other hockey moms on her kids' teams

Fortunately, the Senate has to confirm the appointment.