I don't think so. In WWII people didn't panic and head for the hills when they saw other cities were being bombed.
When a hurricane comes to Florida, people have to be encouraged to evacuate.
It depends a lot on the people you are talking about. Americans carry guns, anyone who acts up is liable to get shot.
There weren't any cities bombed in the US during WWII other than Pearl Harbor, once. In Europe there was nowhere to go unless you had family in the country.
As for having to persuade people to evacuate for a hurricane, some people believe that their home can withstand the storm or the storm won't be too bad so they opt to stay and ride the storm out. No one is daft enough to think they can ride out a nuclear explosion.
American people have guns and so will the hundreds of thousands that fled the city with little more than the clothes on their back and think that it's unfair that you have a warm house and food and they don't.