A declining birthrate has little to do with a culture and people surviving. For most of history, said populations were rising and falling but most often remained stagnant. In fact, for most periods where there is a noticeable spike in population, a lot of economic and social turmoil followed. But the culture survived, as did the people.
No, what the fear of a stagnant or declining birthrate is all about is survivability of the welfare state and many of its institutions. It's about having enough sons and grandsons to fund the current and last generation into their retirement and advanced elderly life. The culture can survive whether or not they are looked after, as in the art of the croissant will not be lost. However, the next few generations will be forced to shoulder a lot more weight financially to support this aging population (forced, because the laws already made and being made are for the benefit of the aging generation). The consequences of this is hard to see, but it may not be pretty judging from the youth reactions in France and all across Europe.
So what is gay marriage to all of this? Certainly, there is a moral police behind much of its opposition. But these, as always, are simply the mobilized voters to call upon for someone else's gain. And not everyone is as morally guided as Santorum (claims himself to be). So what if gay marriage is recognized tomorrow on the federal level and state level? That's, what, 600,000 households now wanting access to the big pot that marriage had normally provided - Social Security, tax breaks, and the recent trend that has tried to eliminate what marriage tax penalties were put into place in the 70's by the baby boomers looking to secure their safety nets. So unless the model homosexual family included a half-dozen adopted children, as a statistic they are a threat. A minor threat, maybe even financially negligible, but a very useful one. Hence the televangelists reminding you to get angry about gay marriage and not get angry about the $712 billion spent on Social Security.
The more you look this way to see them protect the family, the less you'll look that way to seem them protect something else entirely.