I remember that same reaction in my Parents to The Day After. They woudn't let me watch it. It's odd to think back, but the nuclear tension was almost palpable.
I found it playing on TBS or something about ten years ago and decided to watch it, to see what I's missed. Man, what a stinking pile of schlock. I suppose it must have had more impact in the 80's when we were all afraid of nuclear war, but in the late 90's, and I suspect, even today, you loose the message under a pile of syrupy sentimentality and truly bad FX.
That's interesting, because the Wikipedia article makes it sound pretty hardcore.
All I can say to that is, WOULD YOU LIKE TO PLAY A GAME?
www.everybody-dies.com