There were a lot fewer commmercials after the bomb went off on The Day After. Other than that, I don't recall much of that made for tv film. There were other nuclear scare films in the 1980s (When The Wind Blows, Wargames, and Miracle Mile among them as well as the Atomic Cafe documentary).
There were a number of them in the 1950s/1960s too (This Is Not A Test, Panic In Year Zero, Five, Dr. Strangelove).
The Russians almost did launch a mutually assured destruction attack in the 1980s (triggered by a faulty reading). The guy who refused to push the button was reprimanded and the story didn't come to light for over a decade.
Somehow, the liberal anti-nuke crowd never pointed a finger of blame at the Soviet Union. Instead we were told how "bad" Reagan was for America ('how dare he joke "the bombing begins in 5 minutes"?'). While there were Soviet threat movies made in the 1980s, we are told today that the Rambo mentality was wrong too.
Testament is another one I remember from the Eighties. A total load of lib crap, but I have to tell you it was very effective when the emergency broadcast system broke into Sesame Street to warn of a nuclear attack.