What would have happened if the offer was rejected. Cuba would have been assaulted.
I find it unlikely that the US special forces that would assuredly secure the rockets on the island would not get there before Kruschev got word.
Therefore, and for other reasons, I doubt there would have been any atomic attack on the US.
However, Cuba is well defended, and may have been able to punitively damage Florida, in particular Miami or the Keys, and the damage to the US public's opinion of their government would be very different, even if there were no further escalation by the Soviets.
Also, it would potentially be the first time the US was fighting on its own soil since the Civil War, and our nation's psyche would be very different because of it. What do you think would have happened had the offer been rejected?