If JFK had accepted the Pentagon’s advice and invaded Cuba, the results could have been horrific. It is not difficult to envision a desperate local Soviet commander in such a scenario, perhaps cutoff from communications with higher authority, resorting to the tactical nukes at hand to save his command, or at least ensure that its demise did not come cheap. The Red Army, with victory in WWII only 17 years in its past, did not lack military pride or an ethos of defiance unto death.
If the Soviets had used nukes in Cuba, the US intended an overwhelming nuclear response. Things could easily have escalated from there to a full blown nuclear exchange that would have devastated both countries and Europe, irradiated the Northern Hemisphere, and set humanity back centuries. Fortunately, JFK resisted the pressure from his generals and admirals, and relying on diplomacy, back channels, and blockade, successfully diffused the crisis without triggering WWIII.
Where Did We Find This Stuff? Some Sources and Further Reading