The Senate has its own way of dealing with senators that are hated by most in that body. It's known as ostracism, executed by handing the annoying senator lousy committee assignments and then finding someone to primary him in his next election.
In order to be legal, he either has to be born here, or have some form of citizenship paper saying he is, so he would have to show this and if he couldn’t, couldn’t that prove criminal malfeasance?