Actually in 1957 an all out nuclear war with the USSR would not have a Doomsday for the US.
The USSR had no effective way to deliver nuclear weapons to most of the US. The SS-6 rocket took days to launch and they only had like 6 of them. Their bombers lacked the range to hit many US targets in the South and the US actually had SAMs and fighters that defended major US cities.
Add that they would have had to fly over Canada as well to hit US targets and most would not make it. Did I mention that a lot of US interceptors carried nuclear armed air to air missiles?
So New York, San Francisco, LA, Chicago, Detroit, Boston, and maybe Washington DC might have been hit but Dallas/Fort Worth, Houston, Jacksonville, Atlanta, and many others would have been fine.
Today things are very different but at that time number of targets that USSR could hit in the US was very limited and we would have hours of warning.
Europe, Japan, and Korea would have been a much different story.