Actually, the states right argument is the Constitution. If SCOTUS follows the Constitution, they will leave marriage issues up to the states where they has always been. At this point, it’s a toss up, because we all know that they have ruled outside the Constitution many times.
One of Cruz’s bill calls for a Constitutional Amendment to support traditional marriage. It won’t get past Obama, of course, but it can be reintroduced once he is out.
Amendments have absolutely zero Presidential involvement, other than bully pulpit.