I've had similar verbal skirmishes with people at work. I keep calm and usually end things with, “Give me one example of something Obama has done that you could say is proof of his supposed intelligence?” I haven't got an answer yet. One lady really gave me attitude and I told her she could think about it for as long as she wanted and get back to me. She hasn't got back to me.
I challenge people on their b.s. at almost every turn. I'm sure they talk about me behind back but they know they have to bring the goods or shut their mouths around me. I prefer it that way because I'm fed up with tolerating ignorance.