Just to be sure that you understand the Constitutional foundations of the militia. I direct you to something from the above article.
The Congress has the power to nationalize the militia. Which could be considered the Constitutional basis for the draft.
Article I, Section 8, clauses 15 and 16 of the U.S. Constitution refer to Congresss powers concerning the state militias. Clause 15 empowers Congress to call forth the state militias into national service for specific purposes. Clause 16 empowers Congress to organize, arm and discipline the state militias, and to govern the militias while they are in national service. The Second Amendment confines Congresss power by guaranteeing that the Congress cannot govern the militias right out of existence and thereby disarm the people.