None. He could have left the airport any time he wished.
But he isn’t going to the planes until he gets the once over like the rest of us.
Not according to the TSA. They claim that once you submit to the screening, you must complete it.
What really happens when you refuse: they call local law enforcement. You wait until they get there. Then, local law enforcement escorts you back to the non-secured area.
The TSA has no authority to detain you, but they do. The cops know this, and that's why you leave immediately after they arrive.
For those curious, Article I, Section 6, Clause 1:
...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 from the same; and for any Speech or Debate in either House, they shall not be questioned in any other Place.
Section 6
1: The Senators and Representatives shall receive a Compensation for their Services, to be ascertained by Law, and paid out of the Treasury of the United States.6 They 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; and for any Speech or Debate in either House, they shall not be questioned in any other Place.
That directly contradicts Paul's description of the event.