Assume that the terrorist attacks of 9-11 don't happen or are somehow prevented. Assuming the Iraq War also doesn't happen during Bush's first term, then who is the Democratic nominee in 2004? Remember there's been no 9-11, so there's no war in Afghanistan (although the CIA might be supporting the Northern Alliance), no Homeland Security, and most of the issues will be economic or otherwise domestic.
For the record, the candidates in OTL were:
John Kerry
John Edwards
Howard Dean
Wesley Clark
Dennis Kucinich
Al Sharpton
Joe Lieberman
Dick Gephardt
Carol Mosley Brown
Bob Graham
Would the Democrats have gone with someone more moderate to compete with Bush? Without the popularity afforded to a wartime President, it might have been harder for Bush to consolidate the Republican base-would he have faced a primary challenge?