Agreeing that a debt exists and agreeing to pay back a debt are two different things. The budget doesn’t argue whether the debt exists, just how and when it will be payed back. It is the difference between “Yes, I owe you $100, you’ll get it back someday.”, and “Yes, I owe you $100, and I’ve budgeted to pay you $20 a week for the next 5 week until we’re square.”
The consitution guarantees the first part, but doesn’t help much with the second. However, without the second part everything grinds to a halt.