Militarisation affects the entire tone of a culture, and its a dangerous thing to do in a culture that's already so heavily militarised.
If such a draft were in place before Bush II appeared, I can't see any way that it would have made Iraq less of a fiasco. And I can see a lot of ways it could have made things much worse. Because with a pre-existing draft it's likely the US army would now be in Iran, Lebanon, Syria - and probably also Milton Keynes. And Paris.
And as for making everyone fight - deferments happened before, and you can be sure the rich and powerful would find ways to make them happen again.
It may just be me, but during my 4+ years in California I came away with the impression that the US has a very militaristic society and culture. And it begins with the large amount of veterans one interacts with in civilian life. Those whom the Gods wish to destroy They first make mad. -- Euripides