Why? The authority is already, de facto, in place through the constitutional right to raise armies (it doesn't say hire armies or ask for armies), the right to call the militia into service (all able bodied men) and the supreme court agreeing with congress that this is constitutional. If anything, an ammendment would be required to forbid the draft. Perhaps you should try that route if you oppose the draft that strongly since, as it stands now, the draft can be instituted by congress at will.
The Constitution gives the President the authority to call the militia into service. However, the examples of the three Federal military actions I cited indicate that the intention was to call the organized militia, trained, part-time soldiers. That the training and discipline of the militia, including the appointment of officers, was to be a matter for the states to handle indicates that the original intent of the Framers was for the organizing of the militia to be a state matter. In other words, the states had the common law authority to conscript men. This power was not passed on to the Feds in the original language of the Constitution. Further, given the language of the Ninth and Tenth Amendments restricting Federal authority to what was delineated in the Constitution, this power could not be imputed,
Raising an army clearly implied creation of a professional military, such as the European states had. A professional military is one that is a voluntary service, a contractual agreement between the officer or soldier and his government. In the 18th Century, all the European nations, with the possible exception of Prussia, had such armies. That is the context in which the Framers wrote the clause "to raise armies."
That the Federal government utilized the draft in the Civil War, the World Wars, and the Cold War era does not indicate that the politicians were conforming to the original intent of the Constitution. Rather, the approach has been the same "living document" and "implied powers" balderdash that has transformed our form of government from a limited Federal government with most powers resting with the states and people to an almost unlimited central one with the states and people subject to the whims of Washington bureaucrats. If we conservatives decry the abuse of the "implied powers" and "living document" legal theories to establish minimum wages, environmental regulations, affirmative action, etc., we need to be consistent, even when the cause is good, e.g., the raising of armies for the protection of the nation.