The GOP wants to gouge the American economy (via shutdown) and junk our credit (via debt ceiling). Well, who's going to let them?
The Executive branch has a choice to make. It can either pretend that the House of Representatives is behaving as the Constitution requires it; to manage the nation's finances and protect its welfare, or it can refuse to play Calvin Ball with John Boehner. The House can issue censure after censure, but it doesn't have the manpower to actually shut down the government. The Executive merely acquiesces to the lack of explicit funding because that's the way the American political system is supposed to work.
The problem for the Executive (and the rule of law), is that the American political system has failed. A cadre of radicals who don't believe in the basic tenets of republican governance has commandeered Congress. The radicals' leverage is that they have a constitutional responsibility to pass funding bills.
The House has abdicated that responsibility in pursuit of counter-majoritarian, ideological ends. This is an engineered constitutional crisis, and it is time for novel constitutional thinking.
There is a congressionally approved, lawful funding package for the government. The conventional wisdom is that this funding expired at midnight on September 30th. Congress set this deadline for itself in order to renegotiate the spending package. Simply because it has not replaced its agreed-upon spending contract should not prevent the Executive from fulfilling the existing demands from Congress. Contract negotiations extend past deadlines without drastic consequences because parties agree to continue working with the same contract after its term expires. The United States Federal Government should play by these common-sense rules.
And the debt ceiling? The idea of actually enforcing the debt ceiling against the Treasury's bedrock responsibility to pay the bills incurred by Congress is itself novel. The President should feel absolutely no compunction in ignoring the debt ceiling. The debt ceiling is a self-defeating law. Congress implicitly overwrites any enacted debt ceiling every time it appropriates money.
This effectively disarms the radical right. Once their nuclear options are taken away, they may even find it worthwhile to do the job to which their constituents elected them. Until then, who's going to stop the President from keeping the government running? The GOP and whose army?