Ross Douthat had a column in the NY Times in which he noted that, according to Gallup polls, acceptance of polygamy had doubled in the last 15 years and speculated that it would continue to grow. His idea is that "the now-ascendant model of marriage . . . offers no compelling grounds for limiting the number of people who might wish to marry." That is, if you accept the argument "if two people want to get married, why should it matter if they are of the same sex?" then it's hard not to accept "if a number of people want to get married, why should it matter if the number is more than two?" An alternative idea, which he alludes to in a blog post, is that acceptance of polygamy comes from a religious autonomy/anti-government philosophy.
The Gallup release doesn't include breakdowns by group, but in 2008, a USA/Today Gallup poll asked about same-sex marriage and polygamy in the following format: "please say whether you think  The decision to marry should strictly be a private decision between the two people who want to marry, or  The government has the right to pass laws to prohibit or allow such marriages."
This was part of a list including marriages between people of different religions, different races, and one or both partners under age 16. Almost everyone chose option 1 for religion and race. The question about people under 16 is different in principle--Douthat refers to the "now-ascendant model" as "adult autonomy"--so I'll leave it aside (about 80% chose option 2).
About 61% chose "private decision" for same sex marriage, and 28% for polygamy. The questions are somewhat different from the ones that Douthat referred to, which asked about whether things are "morally acceptable," but I'd say they're equally relevant to the general issue. If you think about them, the alternatives don't make much sense: someone who says that same-sex marriages should be recognized by law is implicitly saying that the government has a right to pass laws on marriage. However, most people probably just interpreted the question as "should be allowed" vs. "should not be allowed."
By several things that could be regarded as indicators of liberalism--self rated ideology, views of Pat Robertson, how they would vote in a hypothetical election between Obama and McCain, more liberal people were more likely to regard polygamy as a private decision. People who viewed same sex marriage as a private decision were also more likely to regard polygamy that way. So so far it was going that way that Douthat's analysis would predict.
But there was one discrepancy--more educated people were more likely to regard same sex marriage as a private decision, but less likely to regard polygamy that way. And more educated people who think same sex marriage is a private decision are less likely to see polygamy that way than less educated people who see same-sex marriage as a private decision. That is, more educated people are less likely to draw what Douthat sees as the more-or-less logical conclusion from their views. You could argue that this is just because polygamy is not a live political issue, and that if it became one people would start to sense the contradiction--Douthat implies that in a later blog post. The other possibility is that he misunderstands the "now-ascendent model"--that it does offer what people can regard as compelling grounds to make a distinction.
[Data from the Roper Center for Public Opinion Research]