I think the spark was Prop 8 passing in California in 2008. To say that was a stinging and monumental defeat for pro-marriage equality forces doesn't really say enough to the point, a defeat right in the heart of Blue America and also an attempted reversion of rights. I suppose a cogent war analogy in terms of perceived ramifications might be Churchill and the Fall of Singapore. To this day, I'm still stunned that Prop 8 ever passed. However, I'm not sure that it would've moved quite as fast otherwise.
Without question, I think that was what really galvanized the forces for marriage equality to pick themselves up from a monstrous defeat and retool the arguments for the general public and the courts. The courts were obviously a major part of the battle and the wins basically snowballed until SCOTUS was finally forced to take it up. In that realm, I think there was a perceived nod of approval even before the final decision in that the Supreme Court constantly refused to stay any decisions approving of gay marriage.
The other part of the battle was cultural. Part of it was Hollywood and pop culture of course (think mainstream shows like Modern Family), but also just talking about the issues and being visible. That last part was important because LGBT individuals are your family and your friends. They can even be your children. (That differs a lot from other issues like race. Your own kid can turn out to be gay. As the video link shows, you don't have to come out black to your parents.) And particularly on the marriage aspect, they showed that they're just like everyone else (wake up, go to work, raise kids, and all the other parts of domestic life).
A little stand-up comedy that does make some good points:
link.