The basis for the claimed privilege is Article I, Section VI of the Constitution, specifically this part:
They 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 returning from the same; and for any Speech or Debate in either House, they shall not be questioned in any other Place.
The argument is that searching their offices could lead to interfering with their duties and punishing them for their "speech or debate." It's a thin reed, but it's the argument.
It's a legal truism that bad cases make bad law. The danger is that, once the precedent is set, future members of Congress will be subject to searches specifically to find embarrassing dirt as punishment for their legislative positions. George Bush wouldn't do it, but a President Clinton (Bill, Hill or some like minded despot) surely would.
Since this search warrant was based specifically on a felony investigation and the Justice Department had gone through a months long attempt to compel Congressman Jefferson via subpoenae, which he'd ignored. Further they had been rebuffed by official House bodies when approached for help in obtaining the subpoenaed records. The search was the only recourse and was reasonable. A face saving way out of this, provided by President Bush's 45 day "cooling off period," is for the House and Senate to insist on a procedure for serving the warrants. They'll try to gut the practical effects of a search warrant by imposing unreasonable conditions. If Gonzalez is doing to negotiating, which I believe he will, he won't let them get away with that.
But that's a long way form searching an office of a bozo who had the nerve to call out the Nat. Guard, get two vehicles stuck in the mud, all to rescue his frozen cash in hurricane torn NO!.
That's pretty good probable cause that hopefully will be seldom replicated.