The Speech or Debate Clause is a clause in the United States Constitution (Article I, Section 6, Clause 1). The clause states that members of both Houses of Congress
...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.
Article I, Section 6, Clause 1 does NOT apply to public statements outside of Congress. Lying to the public and making false statements in the media does NOT absolve them from punishment.
Also, one could argue that the whole impeachment hoax is a breach of peace.