I highly recommend reading it since it currently appears to me that there's a fair chance Congress will fail to agree. House Republicans seem to be completely intransigent and unwilling to compromise. Democrats are much more willing to compromise, but if they capitulate completely on this issue, they are going to find themselves having to capitulate on lots of other things too - Republicans will draw the lesson that they can get everything they want by threatening to blow up the government altogether. So Democrats probably should not accede to Republican demands entirely, and the tenor of the news coverage at the moment suggests that they won't.
It's possible that the parties could agree to small increases while they negotiate further when the limit approaches close enough, but it's very unclear that there's any basis for an ultimate agreement regardless of more time. Possibly it may require major damage in the markets before enough minds are changed to make an agreement feasible.
Thus it's very interesting to know what the President's options are in the situation in which Congress has essentially left him with a set of laws that violate the rules of arithmetic. What I took away from the discussion at Dorf on Law is that there is very little relevant case law, thus the relevant passage in the fourteenth amendment:
The validity of the public debt of the United States, authorized by law, including debts incurred for payment of pensions and bounties for services in suppressing insurrection or rebellion, shall not be questioned.stands almost unadorned with subsequent precedent. It's meaning is not something that eminent law professors can then easily agree on - questions as basic as whether social security payments required by law, military wages, payments to contractors, etc are a "debt" that the government is constitutionally required to honor, or whether only explicit treasury bonds/bills etc are "debt" for constitutional purposes.
For what it's worth, from the perspective of ordinary business accounting, payments to subcontractors, employees, etc become liabilities of the business when due, appear on the balance sheet as such, and if they aren't paid the resulting creditors can enforce their claim against the business in court, up to and including forcing bankruptcy. In short they function exactly like any other kind of debt. It's not obvious to me why the government should be different.
For another analogy consider what would happen to you as a consumer if you continue to pay your mortgage and credit card bills but stop paying your utility bills, phone bills, medical bills etc. I think you would find that after a short pause your credit score would start to decline rapidly (as well as finding yourself with no electricity or phone service).
But then other questions arise. Is "failing to pay it on time" the same as "questioning the validity"? One might imagine the government readily agreeing - ie not "questioning" - that the debt is "valid", but nonetheless taking the position that it could not actually pay up at present.
The legal situation being unclear would operationally mean that the President would have to make a decision in a vacuum, and then some time later it would wind up in the Supreme Court where Anthony Kennedy would ultimately decide whether his approach had been correct or not.
At any rate, it does appear that the Republican party has been quite innovative here: this is an entirely novel risk to civilization, but nonetheless it does seem to be at least distantly possible that it might now rise to that level, since I don't think anyone really understands the modern global financial system well enough to say what will happen to it if the US government is considered to have defaulted on its debt. But we do certainly know enough to say that modern economies won't function without a working financial system.
Hopefully Congress will step back before they take us over the cliff. Hopefully they understand exactly where the edge of the cliff is - I'm not sure I do.