Tower closures would not necessarily result in airport closures, because some aircraft can land without ATC help, and those that need controller help can communicate with more distant FAA facilities.

CNN: Airport towers get temporary reprieve

Tower closures would not necessarily result in airport closures, because some aircraft can land without air traffic control help, and those that need controller help can communicate with more distant FAA facilities.

CNN: Airports can make case to keep their control towers open