Well two things. One I've said before. We invented the military-industrial complex and pretty much since WWII the military gets what it wants, and it does not want this. They may have some mass conscription in Finland, but as you know, it requires that the military take people like you Dark Lady, and I assure you that the U.S. military does not want people like you in it. It wants highly motivated gung-ho types, not a couple million people who would rather be anywhere else.
Two. Joe Lieberman is a joke. The Republicans don't trust him (because he can't be trusted) and the Democrats think he is a turncoat (which he is), and he is only barely in office as it is. So his sponsorship is not a positive deal. And, at any rate, providing for an increase is not a mandate to increase.
It would open up so many problems and debates - serious social issues, like do women go? Are gays exempt? - that I don't think any sane person (and there are a few left in D.C.) would go there.