I don't think he has a shot in hell either way.
But yes, I think it's unconstitutional.
As a side story, I live in Kentucky at a fairly religious workplace. Also, a fairly conservative workplace. I asked a PM here at the office if he had watched the debates the other night and he said no, that he'd seen highlights on the news. Then he said, "They were going after that one guy pretty hard...what's his name? The poop guy."