This is exactly correct, and it's why so much of the dramatic talk around the debt ceiling is so sensationalized and misplaced.
The president must pay these debts. All of his threats of default are just playing it up for the cameras, political theater, that far too many of us are buying into.
It would be illegal and unconstitutional for the president not to pay these debts. It would be impeachable for him to refuse this constitutional requirement.
And yet day after day this administration is out there threatening to do exactly that to try to gain more power to borrow.