Actually, what he's calling for can't be "unconstitutional", because what he's calling for is a constitutional amendment, which would obviously rectify any such conflict.

Adrenachrome is right about the position of mariage in law. There's nothing stopping homosexual couples from having a mariage cerimony in a chuch that will allow it, and exchanging vows, plenty of homosexual couples do that already in states that don't allow homosexual mariages; the only thing this effects is their ability to claim married status on legal forms.