How does walking out of Congress help get the surveillance act approved any quicker?

Today the House Republicans walked out on a contempt of congress vote against the Imperial White House because they were upset that Democrats were not discussing a bill to extend eavesdropping beyond its present deadline instead. How does walking out speed up the process? Yes, of course, eavesdropping on American citizens is far more important to the GOP than investigating the improper firing of judges, but the House could do both.