If the Republicans force a default it will come back to haunt them. A quick look at the daily inflows and outlays of government cash show that the elephant in the room is Social Security payments. If all other outlays were cut there would still not be enough revenues to cover SS payments, and conversly if you deferred or delayed SS payments all other cash obligations could be met easily.
Based on that simple observation the only rational way to prioritize cash flow without borrowing would be to suspend SS payments. Then the dems will paint the GOP as sacrificing the elderly to protect tax cuts for the wealthy and subsidies for big oil and corporate tax loopholes. This will be devastating to the GOP as the elderly are a substanial part of the GOP's base.