First cousin marriage is already legal in quite a few states. Including Alabama, which surprises nobody.
However, I've yet to see any call for expanding such a thing. I don't think it's comparable and I really don't see it happening.
From what I understand, though, you're right about the genetic issues between first cousins being minimal. The problems only really occur in sibling or child/parent couplings, and even then I think it's only really problematic when done over several generations. (which those..types.. seem to be prone to) But hey, that's for them sciencey types to figure out.