It would take an amendment to the Constitution itself.

Right now, there's a clause in Article 1 of the US Constitution, called the "Speech or Debate Clause," which says, oh, hell, I'll just quote it:

...shall in all Cases, except Treason, Felony, and Breach of the Peace, be privileged from Arrest during their attendance at the Session of their Respective Houses, and in going to and from the same; and for any Speech or Debate in either House, they shall not be questioned in any other Place.
Long story short, that would need to be repealed.