So far as I can tell, the only provision in the US Constitution about possible criminality for Congresscritters is the passage in Article I, Section 6 (quoted above) which makes clear that Rep. Jefferson could be subject to arrest for a FELONY. If he can be arrested for a felony, and an investigation has indicated that he likely committed said felony (don’t know if it was official “probable cause” but they did find $90K unaccounted for in his freezer!), then how can anyone think the US Constitution bars a search of his office and effects. These Congresscritters are not exempt from criminal laws, though they like to think they are..... if the US Constitution allows for him to be prosecuted for a felony charge, then surely it is allowable to conduct a thorough investigation regarding such charge(s).
http://www.law.cornell.edu/constitution/constitution.articlei.html