A reader doubts it:
It's a very surface-level analysis that says gays were the reason for Obama's reelection. Yes, they could have been part of the critical coalition in FL and OH. But not VA, and not CO. Obama could have lost FL and OH, and still comfortably won the election.
The other missing piece of the analysis is very difficult to ascertain: the cost Obama paid in terms of people who didn't vote for him because he supported gay marriage compared to those who voted for him because he spoke up to support it. It seems as though the former subgroup is getting smaller, certainly smaller than 2004, where this issue helped GW Bush carry OH (which unlike this year, turned out to be a crucial state). I think it's good policy that Obama has to support gay marriage, but I don't think there's good evidence that the gay vote was the crucial piece of his coalition.
Another:
Yes the gays were responsible, just as every other subgroup that also voted for Obama in large numbers. African Americans certainly were responsible (and there were more of them than LGBT in all four of the cited states). Working women were responsible (and there are more of them than either African Americans or gays). Presidents win because of total groups, not just because of small niche demographics.
The Dish 