My little town in northeast Oklahoma, population 3500, has one ER nurse and one physician’s assistant or doctor, in our very small hospital. So, they could easily get overrun, but haven’t heard that they have. BTW, the ER staff are excellent. Larger hospitals 30 plus minutes away.
The entire population of the county I live in here in Texas is a little over 23,000 people. We have no hospitals at all in the county. Any hospital care and we have to go to a city in an adjacent county. We don’t even have emergency clinics. Although we do have a doctors office or two.