They really don't have a legitimate case. In Texas it was made illegal for a gay couple to adopt a child. The law was passed thanks to research that said gay parents were more likely to abuse their children than a heterosexual couple. This was later found to be flawed and completely false research from a christian research group.
There's no way that they can ban Gay Marriage and hope it lasts. If they did it would only be repealed shortly after (much like good 'ol Prohibition).
(Plus their whole argument on how legalizing gay marriage will lead to polygamy and bestiality is both untrue and fucking hilarious)