Well, first of all the Founding Fathers -all of them- were dead before the ratification of the Fourteenth Amendment, so your reliance on them for the question of the constitutionality of gay marriage is clearly misplaced.

Eventually, laws forbidding homosexuals the right to marry (a fundamental freedom) will be challenged on the basis of the Due Process and Equal Protection Clauses and probably the Ninth Amendment. It wasn't until 1967 when the Court recognized a constitutional right for biracial marriages. Opponents of the court's ruling used similar insipid arguments that there is nothing in the constitution allowing such an unnatural union and that it would bring about the ruination of civilization.