Well, you are probably right that the national government has no power to regulate marriage in the several states; however, it does have the power to regulate the implementation of Full Faith and Credit under Article IV.
But this is beside the point. This issue at hand is state laws and state constitutions. The constitution does not have to grant an express power to the state for the state to have that power. The Tenth Amendment states: "The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people."
Further, the Supreme Court has recognized in both Maynard v. Hill (1888) and Loving v. Virginia (1967) that the regulation of marriage is well within the police power of the state. So the ruling precedent is that state regulation of marriage is constitutional.
I reposted this because this is a good point. Under the reserve powers, marriage does technically fall under the jurisdiction of the States. But they we have to ask ourselves then if it is okay for the majority in the States to force their morals and beliefs on the minority. It wasn't okay after the civil rights movement. So how exactly is this any different? Homosexuals can't choose to be homosexual any more than I can choose to be white. Again, how is this any different than in the nineteen fifties?