It only worked for the Texas demonRATs because the GOP legislators alone did not constitute a quorum, so they prevented the legislature from being able to conduct business. (They had to flee the state because there was a law that allowed the Texas Rangers to arrest legislators and bring them to the capitol to force them to conduct business.)
I’m not sure what the Senate and House rules require for a quorum. If in either house the demonRATs plus one Republican would not constitute a quorum, having the entire GOP delegation refuse to turn up, except for one who makes a quorum call would be a way to completely shut down Congress.
According to Article One of the United States Constitution, the United States House of Representatives and the United States Senate each have a quorum of a simple majority of their respective members. The Senate has the additional requirement in Rule VI of its standing rules of a “majority of the members duly chosen and sworn.” The only exception is when either house sits for choosing the President or Vice President when the electoral college fails to obtain a majority vote. In this exception, each house requires the presence of members from two-thirds of the states to satisfy quorum.http://en.wikipedia.org/wiki/Quorum
If nothing else, it would get good air time from Fox and local stations. Publicity would not hurt.
They should be arrested upon their return for ‘evasion and flight to avoid prosecution’.