Edited: I couldn't find a "reliable" source (i.e. actual case copy) refuting the governments ability to draft. If you find something more substantial than a email that says "Willie retained his civilian status. The court ruled that the draft law required some definite ceremony to transform a civilian into a soldier. As the Army decided to have one step forward constitute the ceremony, and Willie didn't take the step, he wasn't a soldier. -- U.S. Court of Appeals, 1954". In fact, the only cases involveing the goverment ability to draft give supporting points of view. Therefor, I apologize for the inaccurate information, and retract that portion of my post.

http://www.sss.gov/FSwho.htm - Its all persons, legally or illegally in the US, over 18 and not yet 26. There are exceptions to this, but even Consceincous Objectors must register.