The Cuban Missile Crisis, which occurred about 50 years before the writing of this, is considered the one period in history when civilization almost ended in a global thermonuclear war.
A miscalculation on the part of one side or another could have made that happen.
The Kennedy School at Harvard has a good website that discusses the chronology, the causes, and the effects of the Cuban Missile Crisis. In summary, the crisis started when then President John F. Kennedy discovered that the Soviet Union was deploying intermediate range missiles on the island of Cuba, placing within range a great deal of the United States with weapons of mass destruction that would hit their targets a few minutes after launch. In effect, the Soviets were proposing to alter the balance of power by targeting the United States with first strike weapons.
Faced with the choice between doing nothing and declaring war, with a bombing campaign to be followed by an invasion of Cuba, Kennedy choose a third option that involved a “quarantine” of Cuba, blockading it from military material, and hard-nosed diplomacy. In the end, the Soviets agreed to withdraw the missiles and war was averted.
But what if things had gone the other way? What if the crisis had gotten out of control into a full scale war?
There are two examples in alternate history fiction that examines the question.
In “The World Next Door” the late Brad Ferguson imagines a world reduced to tiny communities eking out a precarious existence in a world poisoned by radioactive fallout. Kennedy is apparently still alive in 1990, the time of the novel, existing in an underground bunker, but writ does not run very wide.
“Resurrection Day” by Brendon DuBois takes place in a world ten years after World War III happens as a result of the Cuban Missile Crisis. A number of American cities have been destroyed, but the United States as a political entity survives. The Soviet Union has been destroyed and the resulting radioactive cloud has killed millions more in Asia. Great Britain, having regained its confidence, has become the sole world power, even requiring some of its empire. One of the plot threads in the book is a plot by certain elements in Great Britain to annex the United States, in essence making it a colony again.
Of course, at least in the history we live in, both the Cuban Missile Crisis and the Cold War ended without the missiles flying and the mushroom clouds blossoming. An entire generation has grown up who have not had the nagging fear that at any moment everything could end. To be sure, there are other fears, from hyped ones like global warming to real ones like nuclear terrorism. But thus far (barring the appearance of a killer asteroid) the end of the world, which might have happened in Oct, 1962, has been postponed indefinitely.