My proposal would be an act "Returning Sacred Marriage to Those of Faith", except with some fancy acronym that would make everyone want to vote for it. The whole argument would be that marriage belongs to the churches, and they should be in charge of it; marriage licenses would end, and churches could issue marriage certificates, which the couple would take to the court house to register their union.
The words "civil union" would have to be avoided, of course, due to their association with gay rights, so something like "domestic union" would have to do -- note that both those words come from the traditional Christian marriage ceremony!
Then after some period of time, like a presidential term, another act, "Equality in Domestic Relationships", would come along and say that any individuals who were entering a "domestic union" could be issued a certificate that would be taken to the court house, and their union be registered just like marriages. That would cover all the not-quite-church organizations which do marriage, and incidentally cover gay unions as well.
Ideally I'd have "registered union" for the legal term, because it indicates that the government's function is merely to record and keep track of unions that people have decided on. People of whatever gender (and number) would solemnify their union in whatever manner and place they chose, take their certificate to the
designated government place, and show it; the government person would merely register them as having entered into a union.