Well I have proof that embracing gay marriage won't help much in my state, Ohio, at least. 60% oppose a law allowing same sex couples to marry (civil unions are evenly divided). Among those who know someone who is gay, 53% still oppose. Moreover, even among those 18-34 52% would oppose such a law.
http://www.quinnipiac.edu/x1322.xml?ReleaseID=1346
The thing about Gay Rights, and not getting this is one reason the GOP is in so much trouble, is not really about Gays or actual rights, or issues. There are a whole lot of voters who are not Gay, don't really support Gay Marriage, and yet find it unseemly for a politician to make a big deal about opposing Gay Marriage. Its really quite odd, but its basically a type of metric for determining if someone is a nasty person. And far more voters than those who actually support gay rights think politicians who oppose it are mean and nasty.
This is sort of the same way that during the 1990s any Republican who was Pro-Choice was automatically a moderate regardless of other issue positions. The whole thing is weird side effect of the way voters use cues as short-cuts to conclusions.
A good example of this is California with Prop 8. Clearly a majority of voters voted for it, but open support for the Proposition is a fringe position in public, and given the climate of the last few months it mus be even among many of the people who voted for it. Its pretty clear that Meg Whittman is going to have serious trouble in the General Election from her support of Proposition 8.
Part of the reason for this is that the Civil Union position, while superficially appealing, is intellectually unsustainable. If one is religious enough to oppose Marriage, and buys the arguments about weakening it, one should naturally oppose Civil Unions as well. In turn, once someone has legitimized in their own mind that Gay Relationships are equal and deserving of equal recognition it is a very small jump to full marriage. Therefore, while it is a position that appeals to voters in their own minds, it sounds spectacularly condescending or dishonest when proposed by a politician.
The GOP can get by without being the Pro-Gay Marriage party. It will take enormous damage however from being the Anti-Gay Marriage party.