But What Can They DOOOOO

There are many options, but I think obscured (deliberately) is that not paying the bills, or even prioritizing paying the bills, is probably the less obviously legal thing.

If there is a lawful action that simultaneously avoids both a breach of the debt ceiling and a default that violates Section 4 of the Fourteenth Amendment, the Treasury has a duty to pursue such action to the fullest extent. There are in fact multiple Constitutional constraints and considerations that the Treasury must take seriously right now, including the potential relevance of the Presentment Clause and separation of powers principles. All of these considerations make default and 'payment prioritization' highly disfavored outcomes even on legal grounds, leaving aside the catastrophic economic implications. And the fact that Treasury appears to be operationally unready to undertake such lawful action—even though the debt limit was functionally reached over four months ago—is an act of constitutional malpractice of the highest order. We sincerely hope the Treasury is taking operational readiness more seriously than meets the external eye.