Historically, the results of ballot initiatives involving marriage equality (for example, California's Proposition 8) have been less favorable to equality than polling would suggest. The most commonly advanced explanation for this discrepancy is social desirability bias (popularly but incorrectly called the "Bradley Effect"; see Dave In Northridge's explanation for why the term is incorrect): opponents of equality know their position is unpopular and thus are unlikely to state it to pollsters, causing polls to overstate support.
However, the results of the recent Washington Post/ABC News poll suggest that this isn't the case, and that if social desirability bias is having any effect, it's causing polls to understate public approval of marriage equality.
One of the questions in the poll asked respondents whether they thought marriage equality had majority approval in the US. Overall, only 34% of respondents answered yes. Since 59% of respondents approved of equality and 41% disapproved, this means that a substantial proportion of the population approves of marriage equality but believes their position isn't a popular one.
The poll cross-tabulated this question with level of approval for equality. 57% of those who "strongly favored" equality correctly thought they were in the majority, while only 39% of those who only "favored" it did.
Things get even more interesting when you look at opponents of equality. 78% of those who "opposed" and 81% of those who "strongly opposed" incorrectly believed they were in the majority. This goes a long way toward explaining the ludicrous self-certainty shown by many marriage equality opponents; they truly believe they have overwhelming public support, and thus feel free to say outrageous things.
So there's very little chance that an equality opponent would tell a pollster that he/she supported equality in order to avoid seeming "politically incorrect"; the overwhelming majority of opponents believe that their position is the publicly respectable one.
Proponents, on the other hand, might have some incentive to falsely state opposition, especially if they live in conservative areas, because some of them perceive their position as too radical for public consumption. Thus it's unlikely that, say, someone would have told a pollster that they were planning to vote against Prop 8 when they were actually planning to vote for it.
Consequently, we have to look to other factors to explain the underpolling. One of them, probably the biggest, is that both opposition to marriage equality and likelihood of actually voting in an election goes up with age. The under-30 crowd is the most likely to favor equality and also the most likely to stay home on Election Day. The over-65 crowd is the only demographic that opposes equality by a majority, but it's also the one most likely to be found at polling places.
As an aside, I wonder if there's a sort of "Lake Wobegon Effect" among a subset of supporters where they congratulate themselves on being more progressive than they really are, thinking they're taking a daringly transgressive position when they're really just following "The Establishment".