For one, just because the US constitution does not list a right does not mean it is not one. "The enumeration in the Constitution, of certain rights, shall not be construed to deny or disparage others retained by the people."

For another, LAW protects against discrimination. Of course the constitution itself doesn't declare you have a right to a particular job...but law still says you can't be kept from it by virtue of race, color, religion, sex, or national origin. While not specifically stated, these laws have also been interpreted to include sexual orientation by The Office of Personnel Management. Additionally, it is also illegal to discriminate based on "genetic information", so depending on how one views the "cause" of homosexuality, it could be covered under this as well. This isn't meant to "prove" that the same applies to marriage. I'm giving an example of a right not stipulated in the constitution that is protected by federal law.

The argument against gay marriage is continuously a religious one, but this is not a religious matter. It's a legal matter and religious prejudices are not valid justification for legal discrimination. Your average homosexual couple is not asking for churches to be forced to marry them. They're asking for the same legal status of heterosexual couples.