I don't think Rice would get the nomination. She is great on national security but is way too liberal
on social issues. Maybe for VP
but not for President. Same would hold true for Rudy Giuliani. A fairly good fiscal/foreign affairs conservative but way left on social issues.
If Bush wins in 2004 (which I expect will happen) then the field is wide open on both sides. It won't be Jeb as he has said on multiple occasions he does not want to be President, ever. Also, can you imagine the Democrats mantra in 2008 if Jeb ran for President? "Vote Democrat, Stop the Bush Monarchy/Dynasty".
One name I keep hearing floating around as a Republican candidate in 2008 is Colorado Governor Bill Owens but of course it is way to early to speculate.
On the Democrat side, it would be another wide open field. If 2004 is another close election like 2000, then Kerry could possibly run again. John Edwards and Al Gore are another possibilities but I would put my money on Hillary running in 2008. For that reason, I wouldn't be surprised if the Clintons try to torpedo Lurch's campaign sometime soon after the Democrat convention.