It's much about getting to a bomb shelter in time. Assuming the government is awake and actively monitoring for nukes there's only a few minutes from when the bomb is detected to when it hit's the target, in that time the government will have to sound the air raid alarm, warn everyone via radio and quickly get as many as possible to take cover.

Today it's also probably more likely for the bomb to detonate far up in the sky, causing a long distance EMP, or hit the ocean, causing a tsunami in order to disrupt important coastal cities. Rural areas will likely be fine tho.