Well, who's trying to stop their launch and how long after the initiation of the launch process do they realise the mistake and try to stop? Are you talking about the Soviets ordering a counterstrike, realising their mistake, and then ordering their forces to stand down? Or have the Soviets already launched, the Americans begun to retaliate after detecting launches, and then Washington deciding (why?) to stand down?
In terms of time, there's a big difference between rescinding the go order five minutes after and an hour after - the balance is one glowing hemisphere, more or less.