It seems to me that people's minds aren't being changed, their gut reactions are being changed. This is not a logical contest—the logic has been there ever since we accepted the Enlightenment idea of marriage for love. This is an instinctual battle with people's disgust, revulsion and deep-down aversion to "the other".
That battle is won when gays are humanized, with every friend that comes out, every celebrity that discusses the matter openly, every older person who passes away having always found homosexuality foreign and vile, and every person coming of age for whom it's just not that big a deal because it's nothing out of the ordinary anymore. A victory will be due not to debate, but to the slowly rising tide of familiarity.
I certainly think this is the crux of the matter, which is why all gay people have a moral duty to be out. But the arguments do count in a democratic society; they persuade those with no gut reaction, and they have also persuaded the gays. We forget how unpopular this was when we started this journey. My own view is that when all gays truly believe they have the right to marry, they'll get it. And getting them to believe required a certain amount of, er, debate.