According to CNN, the State Department has released a letter stating that the USA will not issue or renew passports for anyone unless it’s an absolute emergency. The department’s website says that it will only be issuing passports for “life and death” scenarios, and only if the person is traveling within the next 72 hours.
The website also says that you’re still welcomed to apply or renew your passport, but if you do, you should expect “significant delays” and they recommend you just wait until the pandemic is over. This means the delays they speak of will most likely be months, until their offices are fully staffed again.
If you feel you do have an emergency, visit the State Department website to see what qualifies as an emergency. The website says that they are only considering “serious illnesses, injuries, or deaths in your immediate family” and that extensive documentation will be needed to prove your case.