I'm not quite to this point of cynicism. I think the GOP would love to show people they can live without Big Government. They all have a job whether our budget is 2 Trillion or 2 Billion per year.
The GOP members have their jobs because the voters want someone in DC to limit the scope of government. The Dems are there because their voters want government hand-outs. Of the two, the GOP benefits from a shutdown because their voters won't be affected while the Dem voters will meltdown (and probably riot but that's going to happen anyway when the US goes completely bankrupt).