Republicans have everything to gain. It is a complete win win for them.
If they let the country default on the debt, come election time they can say "The United States defaulted on its debt for the first time in American history under the control of the radical, irresponsible Democrat party, Vote Bachmann!"
Or if they do get the spending cuts they are calling for, come election time they can say "Obama and the Democrats enacted the largest cuts of social programs in American history, they hate old people and poor people! Vote Bachmann!"
Of course the expected reaction from the Left is to simply roll over and let this happen like they always do, and this is a common theme for the Democrats, but I hope that if it was taken this far they would feel the need to do something about it.