That's true until it isn't. I hope you're right, but I worry that you're probably overestimating our politicians. They're not all playing 5D poker. Some are just plain stupid.
Our system of checks and balances didn’t really account for what happens when a sizable minority in government are bent in destroying it.
So, Treasury decides to punch through the debt ceiling. What happens next?
The US has defaulted on its debt several times.
For example FDR defaulted on the debt when he refused to pay back bonds denominated in gold with their face value and instead paid them back in devalued currency. The Supreme Court ruled that he had acted unconstitutionally, but also did not force the government to pay back the full value as FDR had said he would ignore such a ruling.
The debt ceiling debates every year are certainly theater though.
And it's not theater. When these debates occur the legislature is forcing the executive to face taking extraordinary steps. That's leverage used to negotiate budget deals.
Thus, the "extraordinary steps" I mentioned. Some have argued the executive has the authority to do any conceivable thing necessary to ensure that the "validity of the public debt ... shall not be questioned," to include ordering the Fed to honor Treasury overdrafts.
Another extraordinary step by the Treasury would be minting legal tender and depositing it with the Fed. The so called "trillion dollar coin" scheme.
At the end of the day they'll do what they have to do. This story makes it very clear that the Fed is not interested in becoming the political target over US default, so don't imagine they're going to take some heroic stand.
The Treasury hasn't come close to proposing over drafting. It would sell Treasuries and then have cash. If that became problematic, it would mint. The Fed cannot, by law, lend money to the Treasury. It can't even purchase Treasuries from them directly.
We'll see.
Others argue minting is more palatable. I think legally that's true. I think politically that's false: there is a visceral reaction to any talk of "printing." The various euphemistic ways the Fed can handle it will be preferred. Of course it will end up in front of SCOTUS, but that's a political win: SCOTUS becomes the bad gus trying to "destroy democracy". Or something.
The point is it’s unnecessary.
What does this mean? Even if a Treasury auction fails, the Treasury has the power to mint currency. It could literally just deposit paper representing the $200bn of gold at Fort Knox and have money in its Fed account.
Minting is more precedented than the Fed. Functionally doing this is trivial. It's legally asserting the supremacy of the 14th Amendment over the Public Debt Acts.