ABC News actually gets the story right, here:
The U.S. Constitution actually protects federal lawmakers from detention while they’re on the way to the Capital [sic].
“The Senators and Representatives…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….” according to Article I, Section 6.
The Senate is back in session today at 2 p.m., with votes scheduled at 4:30 p.m.