IANA economist, but if there were a debt crisis, it would ultimately be about the psychology of the investors who would buy government debt. They want to be very, very confident that they will be paid back (which is why they're willing to accept a low interest rate).
If those investors are satisfied with a return to a late-80s fiscal posture, then great. But if they're worried that spending would just creep up again once the pressure is off, they might "demand" further cuts.
In particular, investors often like to see the contrast of infrastructure development (investing in future GDP), as opposed to paying day to day operating costs, retirements, interest on debt (never mind larger debt as far as the eye can see), and other creative ways to prevent future GDP. And there is very, very little infrastructure development in US budgets.
If those investors are satisfied with a return to a late-80s fiscal posture, then great. But if they're worried that spending would just creep up again once the pressure is off, they might "demand" further cuts.