What if Republicans refused to show up for the vote and they didn’t have a quorum?
It does have precedent.....from Wiki...
Quorum-busting in the United States A prominent example of quorum-busting occurred in 2003, when the Texas House of Representatives was going to vote on a redistricting bill that would have favored the Republicans in the state. The House Democrats, certain of defeat if a quorum were present, chose not to be present in the House that day, but instead took a plane to Oklahoma, preventing the bill from passing due to a lack of a quorum. Legislative bodies often have rules to discourage quorum-busting. In many U.S. legislative bodies, such as the United States Senate and House of Representatives, if there is no quorum present a call of the house could be ordered, which would cause absent members to be arrested and brought to the floor of the body. This was the reason that the Killer D's fled to Oklahoma, which is outside of the jurisdiction of Texas law. The Killer D's effectively killed the legislation by staying in Oklahoma long enough to let the legislation expire.
The same year, the Texas Eleven, of the Texas Senate, fled to New Mexico to prevent a quorum of the Senate to prevent another redistricting bill during a special legislative session. Though the Democrats stayed in New Mexico for 46 days, one returned to Texas, creating a quorum; because there was now no point in staying in New Mexico, the Texas Eleven Minus One returned to Texas to oppose the bill with votes in opposition. The bill ultimately passed both the House and the Senate as the 2003 Texas redistricting legislation, which was ruled constitutional by the US Supreme Court in 2006, though Congressional District 23 was deemed an unconstitutional case of gerrymandering.
The technique of the disappearing quorum (refusing to vote although physically present on the floor) was used by the minority to block votes in the US House of Representatives until 1890.