It was well understood what might occur next, at least among the literate - though rarely overtly addressed in media. This was a direct face-down with Khrushchev (who had previously near-humiliated the new President in a naive exchange, at a first meeting).
SAC bombers were all in the air; options included.. what could only be accurately described as H. Kahn's spasm war, and those who knew technology: understood fully what *might* actually occur.
Fortunately for all higher life-forms, Khrushchev possessed a heart as well as an intellect. For it ALL WAS up to: Nikita Khrushchev and the Presidium of the USSR. We had made our response to his stimulus evident. I deem Khrushchev the wiser of the two leaders, in the near-END. He alone - prevented near-annihilation. That should have been close enough.. for ANYONE, and surely is a major reason for the restraint all those next years. Perhaps in retrospect: it was a Victory for us all.
('nuclear winter' had not yet been coined; certainly its prospect was not envisioned even amongst the techno- intelligentsia of '62. Maybe there also weren't quite enough active missiles to achieve that epitaph for homo-sap repetitive folly. But that fact would have been incidental to the ego-battles.)
39 years later .... ???