To keep this short and simple, Congress passes laws mandating that the Administration raise a certain amount of funds. Congress also passes laws mandating that the Administration spend a certain amount of funds. Congress also passes laws mandating that the Administration borrow a certain amount of funds (at most). When there is a conflicting gap between these three, the Administration must first turn to its other powers to satisfy the law and then, failing that, argue in court that the laws are mutually conflicting, resulting in one of them being struck or the court providing guidance on how to behave so as to remain within the law. The Administration does have the power to fill the conflicting gap, though, and it is through the creation of new money.
This may seem distasteful to some, but it is the law: If Congress fails to raise the debt ceiling, then it is mandating -- via the constitution -- that the Administration create more money to satisfy the law. For the Administration to do anything otherwise would actually be to make a far more extralegal and chaotic move.