The last thing the military wants is a draft. The quality of the fighting force would drop dramatically. You won't find anyone in any of the services that is in a position of manning that service nor anyone in the service leadership, military or civilian, who would support a draft. The last thing they want are people who are not committed and don't want to be there.
But I didn't say anything about a draft. I was thinking of something along the lines of the old WPA programs, except gear them toward young adults.