Lieberman strikes me as both a shrewd choice for Veep and a likely candidate to get it. Republicans have been largely discredited, so their best chance is to persuade the public that the Democrats are not a legitimate alternative. Lieberman, as a nominal Democrat, would have the best chance of making the case that his party has been taken over by a left-wing fringe. Indeed, that's pretty much what he's saying now. In fact, I think he's trying to set himself up to run on the GOP ticket in 2008.
I want to say that, as someone who supported Jim Jeffords' party conversion in 2001, I think Lieberman has every right to leave the Democratic Party and run on a GOP ticket if he sees fit. But we shouldn't delude ourselves--him and Giuliani on a ticket would represent an endorsement of the Bush foreign policy in which Americans have largely lost faith. The only question is whether or not Americans will know what they're voting for. And that will require the media to resist the easy narrative about a "moderate" GOP ticket, and point out that on arguably the most important issue facing the electorate in 2008, Giuliani/Lieberman would represent the status quo. If they're going to run that ticket, Americans deserve to know what they're being presented with.