The Supreme Court ruled long ago that the draft does not violate the 13th amendment.
But I don’t agree with that decision, I cannot see how any plain reading of the text does not prohibit it, and forced jury service for that matter. Clearly the amendment was not intended to apply to either but I’m more a textualist than an originalist.
Anyway, the only people pining for the draft (and/or “national service”) these days are the far left. It would be a GIGANTIC wedge issue, huge electoral loser so it will never happen. But I’d love for Obama to push “mandatory national service” like that d-bag Larry Sabato wants, that would have “millennials” lining up to vote Republican, if there’s a war on their parents would line up too.
I’m a textualist as well, but “involuntary servitude” is a term of art, and it never has been understood to cover military service or jury duty.
Similarly, when the Double Jeopardy Clause prohibits the government from placing a person “for the same offense twice in jeopardy of life or limb,” it does not permit the government to try you twice for the same crime even when the possible penalty does not include the death penalty or having an arm of leg cut off (”jeopardy of life or limb” is a term of art meaning “facing serious punishment”).