Depends on who is in the ring. But doing it to them as a group, I'd call that punching down in most cases.

A lot of the late night comedians keep their jokes focused on the politician and his TV cronies. Any jokes targeting supporters have always been about a specific person because of something they've done or said, rather strictly based on their politics. Ex: Colbert's Seditionists Roundup. Or will say, "supports are of the former president claim..." then offer a direct quote, usually using a clip of the person in question making whatever statement is the butt of the joke.