the exit poll data from the 2012 presidential election by Gary Gates of the Williams Institute at UCLA Law School shows that the votes of the LGBT population (which was estimated to be 5% of the electorate (or 4.5 million votes), more than the Jewish or Asian-American populations) were crucial in Obama's popular vote win nationwide by 3 million votes.
As the above graphic shows, 76% of LGBT voters went for Obama-Biden 2012 while an astonishing 22% voted for Romney-Ryan 2012. So, among all voters the Democratic ticket had a 51%-48% advantage but among non-LGB voters the Republican ticket had a close 50-49% advantage, which means that if there were no LGB voters in the sample or if the margin of support had been significantly lower, Obama would not have won re-election.
Of course, mathematically this is not surprising. When an election is so close (51-48) then any group which overwhelmingly goes for the winning side (LGB voters, Latino voters, African American voters, Asian American voters, voters under age 29) can be considered to have provided the winning margin. But that is also precisely the point of building a winning coalition: identify your base voters that you will win by 40+ points and make sure that they turn out.
Gates points out that the LGB vote was aso important in the Blue team winning Florida:
We can only talk about LGB voters because the exit poll did not ask about transgender voters.
Interesting, voters who support marriage equality also went for the Obama-Biden ticket in large numbers:
It also goes to show that the President and the Democratic party being in favor of marriage equality is a vote-winning position.