Howard Dean, who was the better nominee at the time anyway, would win in 2004 and become President promising to end foreign wars and obviously end the draft.
Depending on the economy, he might also become a one-term president, losing against a moderate republican who can prove that he always opposed the draft. He has a decent shot of winning re-election in '08 though as long as he can prove he has solutions to prevent major economic downturn.
Howard Dean, economic genius, ends the draft, causing an economic boom, combined with Clinton's economic policies, should kind of stop the recession for just a bit.