Winning back the public trust isn’t exactly what a lot of us have in mind for the dumb a... to do. Winning trust would be just too hard and out of character for the lying sos.
First of all, it was an incredibly dumb thing to say, after he straight up lied to the American people for years about this law. People might have even given him the benefit of the doubt if this wasn't personal.
Many of them are going to suffer personally because of the changes Obamacare mandated on the country, and a lot of them will die because of it. You can't "win back" someone's trust after being directly responsible for the death of their loved ones.