As do you. As do I. Congress makes the laws. That's what it's there for.
The way that immunity is taken away is that Congress expels them.
I don't know where you're getting this idea that members of Congress have some sort of super-duper legal immunity until and unless they're kicked out of Congress. Patrick Kennedy, to name just one, is still in the House, and is still under court supervision for DUI. He was arrested and struck a plea deal. There was no magical congressional immunity to make it go away.
A lot of legal concepts that are relevant to this debate are only inferential in the main body of the Constitution.
Recall the Framers didn't really think they needed all that much detail about personal privilege and right in the body, and only reluctantly agreed to amendments where some of it would be spelled out. Their theory was that common knowledge and usage would be enough to illuminate individual rights, or even institutional rights. Notice that we get references to "persons, houses, papers, and effects" in the 4th Amendment, but not in the body.
Still, there's no doubt whatsoever that the Framers would have understood that seizure of a person was not held to be more sacred than the search of a house, papers, or seizure of effects", nor vice versa.
It's been argued here that since all the FBI went after were "papers" and not Jeffeson's body, it was all OK.
Yet, no one went after Patrick Kennedy's papers and effects in his congressional office. Might be some good stuff in there you know, like cocaine, heroin, uppers, downers, bennies and other controlled substances.
So, we might ask why the AG thought fit to raid Jefferson's papers in his office and not Kennedy's. Or, did the AG (or his agents) actually try and ended up with the Speaker not giving his approval.
Might be worth your while finding out why Kennedy is given different treatment than Jefferson, the most corrupt congressman of the last few weeks anyway.