It’s in the Constitution.....................
Yes, Congress was given some immunity relative to speech in the Constitution. Until 1988, Congressmen were protected from defamation/slander/libel charges so long as they we in their seat in Congress. I.e., They had to be speaking in Congress.
This changed in 1988, when the were give broad immunity including speech outside of Congress. Re: https://politics.stackexchange.com/questions/46597/can-us-congress-members-be-successfully-sued-for-defamation
After Hutchinson [v. Proxmire (1979)], a Member of Congress was entitled to immunity for statements made “in his seat,” i.e., on the floor or in committee proceedings, but was liable as other citizens for defamatory remarks in the press or elsewhere outside of the legislative body. This state of affairs changed, however, in 198[8] when Congress passed the Westfall Act, which among other things extended existing tort protection for executive branch officials to “officers and employees” of the “the judicial and legislative branches.” As a result of this legislative change (apparently made without much notice or discussion), Members of Congress were made immune from liability for torts committed within the scope of their office or employment. The key question becomes whether an alleged tort was within the scope. The initial decision on this question is made by the Attorney General (which presents some interesting separation of powers questions). The Attorney General’s certification that the Member was acting within the scope constitutes prima facie, but not conclusive, evidence in a judicial proceeding. If the court finds in accordance with the certification, the Member is dismissed as a defendant and the United States is substituted. For defamation and similar torts, this is fatal to the plaintiff’s case because such torts cannot be prosecuted against the United States. One might think [...] that a Member of Congress is not acting within the scope of his or her office when making “false charges” or “defamatory imputations” to the press. The courts, however, have found otherwise, finding that a Member’s communications with the press are generally within the scope of employment. See, e.g. Operation Rescue Nat’l v. United States, 147 F.3d 68 (1st Cir. 1998) (Senator’s remarks to a group of reporters following a campaign fundraiser); Williams v. United States, 71 F.3d 502 (5th Cir. 1995) (Representative’s interview on a local television station); Chapman v. Rahall, 399 F.Supp.2d 711 (W.D. Va. 2005) (same).