The Federal statutes http://www.fbi.gov/about-us/investigate/civilrights/federal-statutes are very specific:
Title 18, U.S.C., Section 245
Federally Protected Activities
1) This statute prohibits willful injury, intimidation, or interference, or attempt to do so, by force or threat of force of any person or class of persons because of their activity as:
a) A voter, or person qualifying to vote...;
b) a participant in any benefit, service, privilege, program, facility, or
activity administered by the United States;
c) an applicant for federal employment or an employee by the federal government;
d) a juror or prospective juror in federal court; and
e) a participant in any program or activity receiving Federal financial assistance.
You could possibly argue States' Rights, since this statute is about federal issues, but the Fourteenth Amendment would obviate that angle.
What they should be doing is making the case that marriage isn't a right but a privilege, like driving. Civil unions take care of the issue of benefitting from government services, privileges etc. Marriage would, too. And officially calling two same-sex people "married" doesn't really change many other rights. I'm all for same-sex marriage, but I don't think it should be that big of a deal. If rights are clearly defined and marital status is one of the protected classes then what's the big deal?
TeH GayZ R dIsGuStiNg!!!! Oh NOES! It's about bigotry, plain and simple. Straight people find sex with the same sex revolting which is what makes them straight people. Then there are the people with homosexual urges who can't handle their own mental complexity. Everything has to be black-or-white for these people. If the law treats gays as equals then straights are less-than, because equality is impossible for some people. If they're not dominant and oppressive, they're victims and oppressed.
The two religion clauses of the First Amendment pretty much guarantee that the idiotic Right will lose this battle in the Culture Wars. The non-establishment clause guarantees that the government doesn't have to give a fuck what their sky-daddy thinks of teh gayz. The free exercise clause guarantees that they can be bigoted if that really floats their boat, as long as they're not being bigots in subsidized programs. That's the deal they make when they take money from the government. They won't have to perform gay marriages. They can deny marriages between man and man just as they deny marriage between Catholic and Protestant. It's not like gays really want to belong to their narrow-minded churches, anyway.
They just have to grow up and accept that not everyone is a carbon copy of themselves and the world won't stop spinning (yes, it SPINS - the sun doesn't revolve around us, as it turns out) if gay people get married.