This is a topic I brought up several weeks ago in a diary thread, and it's something I want to hammer on a bit more.
Speculating on VP nominees is great fun. What baffles me is why people (including respected pundits and even Kos!) concentrate on the field of primary candidates. It's extremely rare for a vanquished presidential candidate to be selected by the nominee for a VP slot. Bush in '80 was the last time it happened that I can recall, and I can't think when the last one before that was -- LBJ in '60?
There are obvious reasons for this -- first of all the losing candidates look like, well, losers. Second, they're all on record attacking the nominee. Most candidates don't want that kind of trouble. A great example is the whole "voodoo economics" controversy which dogged Reagan throughout his campaign. Obviously he won the election, but it sure didn't help him to have people point out that his own VP nominee thought his economic policies were nuts.
Where do the VPs come from? Look at current and former Senators and prominent Congressmen not running for president. That's where most of the VP candidates come from: Dole, Mondale, Ferraro, Quayle, Bentsen, Gore, Kemp, Lieberman, Cheney. Except for Poppy, it's a 100% record since 1976. It's been pointed out that many of them did have some national campaign experience in previous cycles, which gives them a safer, "pre-vetted" status.
So, don't look for a Kerry-Edwards or Dean-Clark ticket. Not impossible, but it's very unlikely. Look to people with resumes that resemble those of Bill Bradley, Bob Kerrey, Joe Biden, Tom Harkin, or Gary Hart. Possibly Bruce Babbitt, though he was never in Congress. Obviously some of the people I mentioned carry baggage (especially Kerrey and Biden), but they are illustrative of the kind of experience VP nominees tend to have.
My personal prediction: Southwestern electoral politics will be a factor in the selection. If Dean or Edwards is the nominee they will look very closely at Gary Hart (who would fill out some of their national security weaknesses). Kerry or Clark will look closely at Babbitt.