Turns out the Treasury Department can prioritize its spending, can choose to pay debt off first — and not default, not bring about end-times, not destroy the country, etc.
This has been a really weird issue considering that the same Wall St. sharpies crying about the need for a higher federal debt limit (lest a default kill us all) have been the same voices claiming that the state and local debt bomb is really no big deal because meta-governmental entities can always be created which would suck up state and local tax revenue and pay off the debt first, thereby avoiding the default.
For those playing at home then, paying off public debt can be a governmental priority. Just not a very popular one among the tax-and-spend, rent seeking crowd.