Let us grant, for a moment, the left's prejudices regarding separation of church and state, and say that natural law is no basis for civil law. Can we still fashion a useful argument against gay "marriage"? The left, generally, says no: that there's no reason to oppose it outside of religious fundamentalism.
To the contrary, given even a modest appreciation for the purpose of law, even when you discard all religious context, there's still no good reason to endorse gay "marriage." Here's the five-step argument:
1. Laws are promulgated to serve the public interest.
2. The care and disposition of children is a matter of public interest.
3. Heterosexual unions have an innate tendency to produce children.
4. Therefore, society has an interest in heterosexual unions, and is within its rights to attach its impetus to them by way of marriage.
5. Homosexual unions have no innate tendency to produce children and therefore are not in the public interest. QED.
To this, the leftist may object, "But not all married couples have children." So? What is endorsed is the capacity for producing children. Not all people who get engineering degrees go on to practice engineering, either; no one imagines we ought to retroactively revoke engineering degrees financed in part with government student aid for that reason.
Or the leftist (betraying his nominalist prejudices) might argue, "But not all heterosexual couples are even fertile." Sure, but how is the state going to figure this out without running afoul of privacy protections (e.g., inquiring about the state of your uterus) or else making an arbitrary judgment (e.g., couples who are 33% fertile may marry but those who are 32% fertile may not). Hands off my body, dude!
Think of it this way. Why do we have a drinking age? To keep alcohol from falling into the hands of those who are not sufficiently mature to accept the responsibility of alcohol consumption. But how is the state going to assess maturity? Are they going to make you show up for a class, take a battery of psychological tests to assess your affective and cognitive maturity levels, make you wait 6-8 weeks while a group of grad students in psychometrics score them, report the results to the state, and then issue an endorsement to your driver's license to let you purchase alcohol? That'd be insane. We use age as a proxy, as there's a decent correlation between age and maturity. Likewise, there's a pretty decent relation of sex to fertility: in fact, sexual complementarity is a necessary (if insufficient) condition for procreation.
Ultimately, this comes down to: what is the reason for gay "marriage"? If there's no valid social reason for heterosexual marriage, the proper response is not to redefine marriage but to abolish it altogether. Promoting happiness or endorsing love or whatever is no compelling public interest: the state has no business legislating on anything as insubstantial as the whims of the human heart. Even if it were the case, as leftists say, that there were no good reason to oppose gay "marriage," there absence of a reason to oppose something is not itself a reason to support it.
Of course, there is no reason to support gay "marriage." The push for it is just the typical leftist scrabbling for limited resources by wedge minorities in the sunset of Western civilization.