One of the standard things one reads, in pieces opposing changing the definition of civil marriage to allow same sex couples to contract marriages, is: "Next thing they'll demand is group marriage." And indeed, one does read some pieces advocating the legal recognition of plural marriage.
I certainly agree that once you start saying that any "loving, committed relationship of consenting adults" should qualify for legal recognition as a marriage, there's no logical reason why you'd refuse to recognize polygamy as well as "gay marriage", however, I'd assumed that most "reasonable people" didn't go that far. Very few people practice polygamy, a lot of those who do do so in ways that seem pretty undeniably oppressive to women, and advocates for gay marriage are always claiming that they just want a way for same sex couples to have the same public commitment and fidelity as straight ones.
However, perhaps I wasn't taking seriously enough the point I made the other day about how, in the process of rationalizing support for gay relationships, a lot of other sexual morality ends up being jettisoned. I belong to a Facebrook discussion group in which strong supporters of gay marriage predominate, so I put out the question: "Question specifically for those who consider recognition of same sex marriage as a civil rights issue: Would you say that recognizing polyamorous relationships as marriages is a similar civil rights issue?"
The vast majority of those who responded said, sometimes quite strongly, that group marriages should be recognized by the state, and indeed that there were no possible just arguments against doing so. Some of them seemed pretty offended that anyone would suggest that there's anything wrong with conducting a polyamorous relationship.
I've looked around a bit and can't find any polling on this issue. My tendency would be to assume that it's only activists who have taken the marriage redefinition game to this absurd level, but it would be interesting to know how widespread this kind of thinking is.