A second bill, H.R. 368, would clarify that the prosecution of a federal official that begins in state court should be moved to a U.S. district court. The third, H.R. 347, would allow for fines and prison terms of up to 10 years against anyone who knowingly enters the White House or the vice president's residence without lawful authority to do so.

Each of these bills has bipartisan support — they are expected to pass easily later on Monday. When passing bills under a suspension of the rules, they need the support of two-thirds of voting members.

The House quickly considered all four of these bills at 2 p.m., and then adjourned. Votes on the remaining three are expected at 6:30 p.m.