Equal protection of the laws found in the Fourteenth Amendment language is cited in both state and federal claims alleging that homosexuals have the same right to marry as heterosexualsSince that has already turned into an attack on the First Amendment, which it is inherently anyway but of late in the courts, then the answer is obviously no.
Homosexuals can enter into matrimony as freely as all other citizens, and many have done so throughout the ages. There is absolutely no bar to a homosexual marrying if he or she can find a willing partner of the opposite sex.
What homosexuals ought not be able to do is force a complete redefinition of marriage on all the rest of us.