[link|http://www.mainstream.com/nhpolitics/getcase.gillette.html|http://www.mainstrea...ase.gillette.html] is an example of a USSC case involving the draft. (The outcome is that one can't register as a conscientious objecter because you object to the current war.)

I don't know of any cases offhand where a state tried to keep the federal government from enforcing a draft, but I cannot imagine that it would go well for the state. National defence is clearly a federal responsibility in the Constitution.

Cheers,
Ben