A draft would pretty much guarantee a win for the Democrats for at least four terms, it would be political suicide for one party to reinstate that.
That is, obviously, unless the war threatens the US itself, but then we are probably talking about some WW3 scheme where in the end conventional means are irrelevant anyhow. I don't think another draft to hunt down some goat herders or rice farmers at the end of the world would considered a worthwhile target even by the most warmongering.