The problem is the GOP members of the House and Senate are by themselves enough for a Quorum. Article 1, Section Five of the US Constitution clearly states "a majority of each shall constitute a quorum to do business". Thus if the Democrats just all leave, the GOP still will have a quorum and can pass anything they want, the best defense is the Filibuster of the Senate which requires a 2/3 votes (and is NOT constitutional Mandated but been a Rule of the Senate since its inception).
http://www.law.cornell.edu/constitution/constitution.table.html#articleiQuorum fights work best in states that require MORE than a Majority to have a Quorum (Such as Texas). In such a state the Minority party (if it is large enough) can end the legislative session by merely walking out the door. Most States adopted super-majority Quorum to protect geographical and political minorities in their states (Through to my knowledge never to Protect racial minorities).