What you're talking about -- the label -- is really determined by mindset, not by law. You have to change minds (and hearts) to win that vestigal battle, and that's going to take a generation or two.
I mean, you can call it "marriage," but then it'll get the word "gay" in front, and it won't be the same label anyway -- it'll get stuck in a linguistic ghetto. You'll have terms like these in common use:
same-sex marriage
gay marriage
homosexual marriage
lesbian marriage
transgender marriage
GLBT marriage
heterosexual marriage
child-bearing marriage
procreative marriage
traditional marriage
non-traditional marriage
Christian marriage
Judeo-Christian marriage
straight marriage
holy marriage
blessed marriage
sodomite marriage
You see, I'm not a big fan of the adjective-noun labels like these. Usually the adjectives are negative. They certainly are for the existing names:
common-law marriage ("shacking up," basically)
loveless marriage
sexless marriage
broken marriage
marriage of convenience
arranged marriage
open marriage
shotgun marriage
See what I mean?
The (very rough) equivalent, in my mind, is with gender and equal rights for women. There's absolutely no denying the fact that men and women are different -- Mars versus Venus and all that. Women live longer -- a fact which pains us men.

(That's one possible reason why the ERA failed. There were pro-ERA forces who insisted on going beyond changing policy.) But while acknowledging that fact, we (should) confer on both sexes the same rights and obligations, including employment opportunities, child custody, and military service, among others. The language is starting to follow, but that's a slower (and natural) process of evolution. It's already starting. "Housewife" became "homemaker," for example. (You rarely hear "housewife" any more.) Or, in another context, "Negroes" (and the slang version of same) became "African-Americans," passing through "blacks" on the way.