They were so sure the Democrats would give in to their ludicrous action in shutting down the government that they didn't bother to provide themselves an out in case their plan failed (which it has done). Now they are desperately trying to find a way out of the mess they put themselves in -- a way to save face with their political base when they finally have to give in and re-open the government.
But the longer the shutdown goes on, the more the public in general turns against them. As the chart above shows, the public disapproval of the congressional GOP is still rising, and has climbed by 11 points in just the last couple of weeks (from 63% to 74%). The question now is how high that public disapproval will climb before the GOP gives up, re-opens the government, and starts trying to repair the damage they have done to their party's image.
Is their ultra-right-wing ideology so important to them that they are willing to risk the continuing decline (and possible death) of their party?
The chart above was made with information from the latest Washington Post / ABC News Poll, conducted between October 9th and 13th of 1,005 nationwide adults (with a 3.5 point margin of error).