A conservative might not be in favor of state-sanctioned relationships at all. Do you realize that if you can pass an amendment saying marriage is between a man and a woman, you can pass one saying it isn't?
So, lets lose the battle and not the war. If we were really worried about morality/Biblical guidelines, divorce would be illegal. Once the barrier is breached, little is left that can be supported. Laws protecting kids being a prime example of things that can. Was the government founded on certain ethics received from Mosaic law? Sure it was. It was also founded on slavery.
Its hypocritical for us to cite all of the terrible things government does in its daily functions, and then cry for it to protect morals. It can't spend our money but it can keep our religion? It should be out of the business of making preferences, altogether.