The only way it would have a chance in hell is to have provisions that testifying before Congress regarding inquiries involving possible criminal charges automatically carries full immunity or isn't admissible in court as evidence against the witness. They can't legislate your Fifth Amendment rights away, but they CAN make it so testimony isn't "incriminating".
Honestly, I think that provision would be in the public interest anyway. Can you imagine if Congress subpoenaed the head of the Cincinatti IRS office and promised immunity, all they had to do was provide truthful testimony? A "get out of jail free" card can be a hell of a lever.