JFK authorized the Attorney General, his brother, to cut the deal that the US for years thereafter would deny it had ever made, the deal agreeing that the US missiles in Turkey would be dismantled in return for a withdrawal of Soviet missiles from Cuba.
Robert Kennedy wrote the following of the moment of the crucial contact, with Dobrynin.
"We have to have a commitment by at least tomorrow that those bases [in Cuba] would be moved. This was not an ultimatum, I said, but just a statement of fact. He should understand that if they did not remove those basis, then we would remove them. His country might take retaliatory action, but he should understand that before this was over, while there might be dead Americans, there would also be dead Russians. He then asked me about Khrushchev's other proposal dealing with removal of the missiles from Turkey. I replied that there could be no quid pro quo --- not deal of this kind could be made ... If some time elapsed --- and ... I mentioned four or five months -- I said I was sure that these matters could be resolved satisfactorily."
The point, of course, was to be able to say, "we were eyeball to eyeball, and the other fellow blinked," while one was winking to the other fellow.
The memo of RK's thoughts appears on p. 554 of Ferguson's vol. I of the Kissinger biography (though Kissinger was in Cambridge, MA while this was happening).