It would be entirely unrealistic for government to get out of marriage entirely. There are inheritance disputes, child custody issues, splitting assets in divorces, joint credit issues... all sorts of property and financial problems to sort out from marriage that courts are pretty well required for. Where there is ownership involved, there will need to be government involvement to help sort it out.
Secondly, the courts are ruling left and right that preventing two consenting adults from marrying is unconstitutional, so the scenario in the OP is unlikely to happen. SSM is 100% about civil rights. If marriage is a right, then it is a right that must be applied equally to everyone. There is absolutely no way around this. It has nothing to do with pushing an agenda, it has nothing to do with pandering to get votes, it has nothing to do with indoctrinating children, it has nothing to do with making being gay "cool". It's about equal rights. Period.
I see no reason for polyamory (thanks MistressNomad for the clarification between this and polygamy) to be illegal. It's complicated, in terms of inheritance and all those other issues I mentioned above, since it more resembles a corporation than a partnership, but it's not impossible to sort out. Again, these are consenting adults. The slippery slope fallacy about children and animals does not apply, since they are not legally able to enter into contracts, and thus cannot marry anyone. However, this discussion is not about any form of marriage besides SSM. There is no "if SSM is okay, then others have to be okay, too". It is an invalid argument.
Marriage is not a religious institution. It's not even a human institution. Many animals pair off, and do so for life. No single culture or religion can lay claim to marriage as its own. It has been a part of many (if not all) cultures that have existed throughout history in this world. To state that marriage is the sole providence of Christianity is ignorant and arrogant. Many Americans do not believe what some Christians in this country believe, and it is wrong to attempt to force us to comply with your beliefs. And NO, it is not the same in reverse. To prevent you from living how you wish would be to infringe on your religious rights, not to prevent you from stopping others from living how they wish. If you cannot handle that your neighbors do not believe as you do, then you have no place in the United States, a land where everyone is free to pursue whatever theological beliefs they choose.
These are my thoughts on what has been discussed in this thread.