While there exists a natural right to form marriages, and while we have a right to form those marriages without government interference (a negative right), we do not have the right to government recognition of our marriages (a positive right). The State regulates marriage because it is in their best interest to manage the procreative potential of opposite sex couples, not because they have a moral obligation to do so. The institution of marriage is a natural union that exists prior to, and wholly independent of government recognition.
What basis is there, then, for SSM advocates to claim they have a right to civil marriage? While those with homosexual orientations have a right to form same-sex relationships, they have no corresponding right to have their relationships recognized and regulated by the government.
Of course, homosexuals could argue that since the government has chosen to recognize and regulate marital relationships, however, that equality and fairness requires that they regulate both same-sex and opposite-sex relationships. Unfortunately, the equality argument works against them. The principle of equality is that equally positioned parties should be treated equally, but same-sex relationships are not equally positioned to opposite-sex relationships.
Each kind of relationship functions very differently in society. As a rule, opposite-sex couples produce and prepare the next generation of society: children. The very survival of society depends on opposite-sex relationships. That is why society has deemed such relationships worthy of social approval and support. The same cannot be said of same-sex relationships. As a rule, they neither create nor rear children. The future of society does not hang on their relationships. Same-sex relationships only benefit those who participate in them, whereas opposite-sex relationships benefit society as a whole.
If the two relationships do not function the same way in society, then there is no reason for society to recognize them as equal. Indeed, to legally declare two unequal things to be equal, proving them both with the same benefits and name, is unjust. Put another way, not only is there no compelling social interest in regulating same-sex relationships, but to treat same-sex relationships as if they were equal to marital relationships would be unfair. Since marriage is a social declaration, society has both the right and responsibility to limit the institution of marriage to those who, in principle, are capable of forming families, which is what the institution of marriage has always been about.
 Although, unlike opposite-sex marriages, these unions are unnatural, and thus there is no natural right to engage in same-sex relationships. As such, governments can either prohibit or permit such relationships at their own discretion.