This is interesting — coming as it does from the liberal Pew Research Center:
[A] new study suggests that opposition to same-sex marriage may be understated in public opinion polls. Using pre-election polling data in states that have voted on same-sex marriage measures, political scientist Richard J. Powell found that pre-election surveys consistently underestimated opposition to these laws by 5 to 7 percentage points.
Blame “social desirability” bias—the tendency of people to give what they believe is the socially acceptable view rather than disclose their true feelings about sensitive topics, wrote Powell in an article to be published in the journal American Politics Research.
Powell, who teaches at the University of Maine, examined all 33 statewide races from 1998 to 2012 where same-sex marriage measures were on the ballot and where statewide pre-election polling was conducted. In all but three of these states, the ballot question was presented as a ban on gay marriage. He only examined polls conducted within 90 days of the election.