For observers outside the US, the idea of "the national government shutting down" probably seems way way more alarming that it does to most Americans. Almost all basic services in the US are handled by states and municipalities. This includes garbage collection, policing, firefighters, schools, local tax collection, road maintenance, the majority of prisons, most courts, most water and power infrastructure, building inspections and permitting, and many more.
Even airports, the site of a lot of hand-wringing during the shutdown due to the TSA (security screeners) and air-traffic controllers being federal employees, are usually (always?) municipally or state-owned. I have no idea of the legality of these municipalities or the airlines themselves stepping in to pay the ATCs or screeners, but it doesn't seem totally bonkers.