It's not. A motion and a second, and closing the doors is AUTOMATIC. Rule XXI takes precedence even over a Senator who has the floor and OBJECTS to the Rule XXI Motion! No debate, no nothing. Motion, second, CLOSE THE DOORS.
http://www.gpo.gov/congress/senate/riddick/275-281.pdf <- Riddick's Senate
Ok, what's it take to pop out of Rule 21?