Michael New and a few others involved in the gay marriage debate are trying to encourage the right with comparisons of Obergefell v. Hodges with Roe v. Wade.
He argues that we're in a better position with regard to marriage today than we were with regard to abortion in 1973 because supporters of traditional marriage are better organized politically today than the pro-life movement was in 1973. Basically (I would say) Roe v. Wade nationalized social issues like this, and the conservative side of the marriage debate has benefitted from the example and existing political network of the pro-life movement. So, the pro-traditional marriage is better organized, is broader and more collaborative and has more political influence than the pro-life movement did in 1973.
That's probably true as far as it goes and is likely part of a good argument that opponents of gay marriage aren't necessarily headed for the same political fate as segregationists. It seems, however, that you would have to do similar comparison between the 1973 pro-abortion and present pro-gay-marriage side to get a complete political picture.
But even putting that aside, there are two big arguments against optimism based on analogies to Roe v. Wade.
First of all, the pro-life movement has persevered in the political debate because it has framed its argument entirely in liberal terms—it argues that abortion directly harms unborn children and that unborn children should be considered to be part of the human community. The second premise is disputed, but no one seriously disputes the first. There are also arguments that abortion harms the mother as well, but this still remains within the liberal framework. Nonetheless, the harm is less direct and obvious and can be considered freely self-inflicted, so these arguments are likely to play only a secondary role in convincing someone that abortion is a social evil to be opposed. I don't know if non-liberal arguments against abortion were ever commonly made (e.g., it enables fornication and adultery), but you never hear them now, and they are not likely to gain traction.
Unlike abortion, there's no really successful liberal argument (i.e. based only on direct harm) against gay marriage. At best, there are arguments for broad social harm or more weakly associated harms, similar to the harm suffered by women because of abortion. Even if we could make a solid evidence-based case that, e.g., gay unions aren't as good of an environment for kids and more gay unions raising kids is, on the whole, bad for kids (unlikely given how much the academic social sciences are in the tank for gay rights), the harm is too diffuse for the liberation-minded utilitarianism that seems to be operational in these arguments. You can't see any obvious harm in the nice gay couple next door raising kids, so broad statistics aren't enough to deny them legal equivalence with heterosexual married couples.
The other course of argument taken is over the meaning and purpose of marriage. But, in liberal discourse, these are don't actually count for anything against rights claims. Even if they were watertight as a matter of logic, engaging liberals on such matters of logic and definition is purely academic. You would at best convince an individual that his definition limits marriage to a man and a woman. Since the question would remain disputed, it could never stand as grounds for denying a supposed "right"--especially a right claimed by an officially recognized aggreived minority.
What's worse, these arguments get labeled as bigotry. While feminists have worked hard to tar the pro-life movement as anti-woman, it has never really stuck in broader society. An argument based on the moral status of the baby doesn't really have anything say about the mother, so feminists have had to claim that pro-lifers have been disingenuous in their concern for babies: "They won't admit it, but really, they just want to send women back to the kitchen". That doesn't really fly because, to most non-ideologues, the harm to the baby is obvious enough to be significant in its own right and worthy of consideration, at least something to be balanced against the rights of the mother. At best, the feminists can tar pro-lifers as being single-issue obsessed and unconcerned about the needs of the mother and children after their born, but it doesn't seem implausible for someone to be totally on board with women's rights, but hold that they stop at the killing of unborn children. And, in fact, the pro-life movement has always been made up of and led by women as much as by men (if not more), so feminists have also had to claim that half the pro-life movement is suffering from false consciousness. Again, not very plausible.
The arguments against gay marriage don't have these advantages. Even if you've got solid empirical evidence that we shouldn't encourage homosexuality, just reporting unflattering statistics about gays or any other officially recognized victim group (much less drawing policy conclusions from them) is itself considered bigotry, regardless of their truth. Similarly, engaging arguments about the meaning of marriage—since they're already automatically disqualified in arguments against rights claims--can only be excercises in justifying oppression. And, while there are a few gays against gay marriage (and probably a good number that don't actually care), they're not a significant enough portion of the movement to serve as an obvious counter-argument against claims of bigotry.
So, whatever advantages the traditional marriage argument has in the way of political organization, it suffers from serious rhetorical disadvantages. This seems likely to lead to waning influence within the Republican party and "respectable" opinion. Perhaps the best possible fate, barring an unforeseen serious change in trajectory, is something like creationism vs. evolution. Republicans have to make an embarrassing dodge to avoid offending the base when grilled by reporters trying to make them look stupid to the rest of the country, but, otherwise, it will have no political meaning.
The larger difference, though, separating the present from 1973 is that the rot of the sexual revolution, the dissolution of the Church and American society have progressed much, much further. That there even has to be a political movement for marriage shows how much worse things are than in 1973. In 1973, the theoretical and legal groundwork of the sexual revolution had been laid, and pop culture and elite culture were largely on board, but day to day life hadn't followed suit to the degree that it has today.
We're much further down that road now. Even if societal acceptance of abortion and divorce have plateaued or even declined somewhat, fornication, contraception, pornography, cohabitation, etc. have become universal and expected parts of the American way of life. Gay marriage has risen in popularity not just because of the non-stop propaganda, but because it's consonant with the way that most Americans already think about sex and marriage in their own lives.
We're not going to see a viable movement against gay marriage without a viable movement against that broader trend of which it is a part. And that is the only way support for traditional marriage is likely to persist—as a part of a broader movement in favor of traditional religion and sexual mores. The political opposition to gay marriage has tended to bracket the question of religion and the morality of homosexual acts in an attempt to build as broad a coalition as possible based only on the definition of marriage, but it didn't really work, and it won't work in the future. While natural law arguments are theoretically accessible to any reasonable person, in practice one's receptivity to them is highly dependent on religious faith and/or the actual lived practice of the virtues. Without those, they simply have no power to convict.
In practice, we won't have the restoration of traditional marriage without the restoration of Christianity and traditional sexual mores. And that is going to have to come primarily from people living it and witnessing to it. If anything, the public, political angle will have to serve primarily to protect our freedom to do so and defend the Gospel against charges of bigotry that prevent people from hearing it.
