I mean, eventually the debt limit has to be completely ignored or the executive has to break a law.
this is not the adjudication process. the money is already authorized and earmarked for spending, and the executive is legally required to continue paying SS, Medicare, Medicaid, military and federal workforce salaries, etc. etc. etc.
but the fact that the money is authorized to be spent does not mean that the money is in an account ready to be spent; the federal government does not have to borrow money to make this happen.
there aren’t many good options for the WH. on the one hand, congress has already told them “you have to spend money on these things”. on the other hand, Congress has said, “you may not put additional money into this bank account under any circumstances.” one of these things, by the laws of reality, must be ignored.
the least bad option, in terms of the damage it would do to the economy, is probably to ignore the debt limit and say it’s unconstitutional, violates the 14th amendment, etc. could get the votes to pass an increase in the debt limit without going the other way, which is not possible without making a clean bill. there may be a political price to pay just to declare the debt ceiling unconstitutional, but we’ll see.
the alternative, if the US government begins to miss almost any payments, is that the interest rate that the market demands on Treasury bonds goes up. this could lead to many more bank failures.
tl; Dr: Actually, it could be catastrophic to breach the debt ceiling if the WH doesn’t ignore it and tell Congress to screw it. it’s incredibly irresponsible and makes every budget priority the GOP actually has far less likely to happen.