Answer:
First, it's important to distinguish between civil marriage and religious marriage. In the United States, it is perfectly legal for a clergy-person to refuse to perform a religious marriage if the couple isn't qualified according to the standards of their particular faith community.
So far, no opponents of marriage between people of the same sex have been able to come up with a valid, secular (non-religious) argument for restricting civil marriage to heterosexuals. So it appears that there is no definition of marriage that would legally deny homosexuals the right to a civil marriage.