In the scene, Travis Bickle (De Niro) is looking into a mirror at himself, imagining a confrontation which would give him a chance to draw his gun. I believe that scene was improvised by De Niro...
He says the following line:
"You talkin' to me? You talkin' to me? You talkin' to me? Then who the hell else are you talkin' to? You talkin' to me? Well I'm the only one here. Who the fuck do you think you're talking to?"