I don't know if Kerry personally supports the idea of a draft, but there are quite a few Democrats who do. I hope someone will correct me if I get this wrong, but I believe the rationale to be that if we're going to go to war, everybody in America should be willing to "make the sacrifice."
Is that accurate? I know that some of them bring up social inequality, but I can't remember exactly what they say about it off the top of my head (and right now, I don't have time to follow up on it).
The Democrats who support the draft seem to be a small minoirty, though. I'm not sure where Kerry stands.