LBJ => Veep
Nixon => Veep
Ford => Veep
Carter => Governor
Reagan => Governor
Bush => Veep
Clinton => Governor
Bush II => Governor
The pattern here is pretty obvious. Don't nominate someone who's serving in the Senate or House of Representatives. They are considered tainted goods due to their voting record. This means that Hillary won't do. Go find some Governor who's never had to vote on a national issue. Heck, if it weren't for the 22nd amendment, Arnold would be a shoe-in for the Repubs.
The Dems are going to have to find some Governor from the midwest. Or they'll have to have Gore run again.