No, they can't. The Constitution makes no mention of marriage. The federal government is a government of limited and enumerated powers. That is why you need a constitutional amendment. Not for clarification purposes, but to avoid trampling on the document that you claim to be protecting. We needed a constitutional amendment for alcohol prohibition. I'm sure the prohibitionists would have argued that the destruction of the populace through alcohol abuse justifies an end-run around the constitution. I'm unconvinced. I do see homosexual marriage as a more serious threat to the union than alcohol use, obviously, but I don't support exceptions to the rules. The Tenth Amendment has to mean something.
Makes me wonder how we got drug prohibition without one?
Possibly so that there was nothing to repeal after the inevitable failure and no way to stop the 'war on drugs' which has brought us so many surveillance and reporting laws.
Who says politicians don't learn from their 'mistakes'...