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I read this short story as a kid 25-30 years ago at a minimum. Details in my description may reflect that time gap. I'm at a loss for the title or author, but I'd like to read it again as an adult.
The story takes place in the USA, and seems to be contemporaneous to the date of publication, which I guess to be in the mid to late 1970s.
The basic plot is that a large government, military, private institution, or possibly even a rogue player wants to popularize the idea of fighting a nuclear war so that people don’t oppose it. In fact, they want people to actually be excited about it and embrace the possibility.
To foster a pro-nuclear war public opinion, an agent of the organization recruits or forms a rock band. I think the genre was acid rock or late 1960s psychedelic because the descriptions of the band's imagery and live shows reflects that era’s visual style. I feel like there was a spinning wheel optical illusion that would mesmerize people. I remember they kept playing to bigger crowds as the story progressed. The band becomes immensely popular. They end up shifting public opinion and people began demanding a nuclear war, if I recall right.
Here’s a key part of the story (and the thing that made me most scared as a kid reading it). The phrase “Do it, do it. Press the button, press the button!” (or some variant) was either part of the lyrics to a song, or some subliminal messaging hidden in the music, or maybe a chant that the band led the audience in. I know the audience heard it in some way, because they embraced the chant. It all bordered on a mob mentality and I remember being really disturbed that people would be calling for nuclear war.
Story spoiler with additional clues
I think it ended like this. At the height of their popularity, during one of their concerts, they were broadcasting live to a massive TV audience. One of the viewers was a fan of the band, and he also worked in a nuclear missile silo. The music, or chanting, or subliminal messaging made him launch a nuclear missile. I believe the implication was that it started WWIII.