it's not an argument of how much explosive power or even how high a level of dangerous radioactivity, it's more like the effect on the planet's ecological stability. The theory is that if a lot of nuclear bombs went off, then a lot of dust would get blown into the atmosphere, and would get between the sunlight and the earth. the dust particles would become part of the earth's upper atmosphere and would take a long time (years? decades?) to disperse, in the meantime, the surface of the earth would get colder and colder, and things that require sunlight to live would all die, in turn, the oxygen levels of the planet would drop, and the food levels for things that eat plants would plummet too. just throwing one thing out can have a domino effect on the whole system.
They thought this might happen when they dropped the first nucler bomb (probably not the one they used on hiroshima, i imagine test bombs would have been tried out, probably in mexico, first) but you know, truman decided, fuck it, he wanted to kill the japs more than he wanted to survive anyway, and the gods have a sense of humour because he got both in the end.
while we're on the subject read this review of a classic film about nuclear war:
http://www.archive.org/details/DuckandC1951and download the film (ten minutes long) here, look on the left of the page:
http://www.military.com/Content/MoreContent1/?file=cw_cd_story however in my opinion, you will get a lot more of worth on the subject from this book and the film that was made of it four years later:
http://www.toonhound.com/briggswtwb.htm