Ok, President Obama doesn't actually "sing" the song. It's a mash-up of sorts, where someone has edited and pasted together clips of Obama speaking and matched them up with the music from Gaga's song. The song opens with an actual clip of Obama addressing the Human Rights Campaign, where he references Gaga before the song cut-up begins:

[youtube:http://youtu.be/AijEQN6AuRs]