Were it an option, I'd take it as a great opportunity to move to Canada or Sweden. If they weren't drafting anyone, France or the Netherlands would also be quite attractive.
If I were rounded up and brought in to enlist before leaving the US, I'd make full use of homosexuals not being allowed in, refuse to wear clothing, and make advances at all the male higher ups (I might start off easy at first to keep from being arrested, just saying I would have sex with men, and then being more wild if that wasn't enough). Even if gays were waived in, my sanity would likely be seriously in question
For Vietnam my dad was too big and an uncle was too skinny to be forced in.