I suspect the Obama administration is playing this better than Clinton. Clinton raised a huge storm by proposing ending the ban on gays in the military, which was a VERY hot button at the time. Now, instead, Obama and the Dems are taking it a bit more methodically, banning discrimination against LGBT folk - which while it will surely raise opposition from the Right is a far less controversial proposal than the "specter" of the next soldier in the foxhole... oh, you know the tired argument there.
California and some other states already has had an anti gay discrimination ban for about 15 years now. The Dems can point to those cases to show that treating everyone equally doesn't mean the end of the world.