The Federal Reserve can choose to print the money the Government spent. They're not the same entity and they don't have the same goals. If the Government spent the money and the Federal Reserve doesn't want to print it, that's uncharted territory.
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.
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.