The truth of the matter is, I think, they cannot!
Pick any argument they make and they can easily be rebuffed.
Let's look at the top three excuses one at a time:
1) Marriage is an American Institution and must be protected to be just between a man and a woman: Do you talk about 50% divorce rate? That's far from an institution. Also, as long as 2 drunks can get married in a drive thru wedding chapel in Las Vegas, that's very weak ground on which to build and institution
2) Marriage is a gift from God and must be preserved: Do you talk about separation of church and state. See the first amendment to the US Constitution.
3) Marriage is for procreation/children: Then marriage licenses should only be given to fertile couples, and those who are paralyzed, or women who have gone thru menopause may not be married because they cannot have children.
4) Gay marriage will undermine US Society: See the State of Massachusetts. Gay marriage has been the law there for nearly 2 years. There has been NO destruction of society there. The streets are not running with blood, the sky is not falling - life goes on! The concept of Separate but Equal has never withstood Constitutional muster, and it won't here.