Married with immaculate taste: I am not brave enough to take on Posner (I did enough of it, vicariously, in law school). So, I'll just make a few comments as distilled from Eno's comment. Early on in Posner's essay, he notes that the Mass high court found that there was a state constitutional right to gay marriage. I think that is where he gets the notion that the Federal Constitution somehow, perhaps indirectly, grants such a right. I, like you, don't know if that's the exact thrust of the Mass law, but again, who am I?
Looking to public opinion as to what the Constitution allows is a pretty dangerous idea. I mean, on the one hand, sure, if enough people want it, then you probably get the votes in Congress to amend the Constitution. Of course, then you're back at nine people then deciding if what the People wanted was proper in the first place - which then negates the idea that public opinion is a basis for interpreting the Constitution (so basically, you have nine people [well, as few as 5 really] ultimately writing the Constitution - kinda scary).
Let's use a Razor trick and take Posner's example to the extreme. Let's say everyone wants to put Jews into "work camps". The Supremes say this is bad. I mean, does that make the Supreme's wrong, or just technically out of their sphere of influence? As Posner himself says, precedent means nothing at the Supreme Court level. So, making things out of whole cloth shouldn't be a problem. Hell, slavery had tons of precedent.
I must admit, after reading his essay, I'm not sure if Posner is criticizing the author's book, homosexual marriage, or the Supreme Court. Probably all 3.