I've read so many varying histories from the top people on both sides. A Cuban friend said the worst that would have happened would be land war in Cuba. I was certain the world would end. My mom sent me to elementary school after making a big deal that the Soviet ship was going to intercept the U.S. blockade in an hour. I begged to die at home. No such luck.
All we did at school was listen to propaganda and practice air raid drills. Imagine grade school kids in Newark, NJ ( a few miles from Manhattan) croucihng and covering our faces with our hands and elbows. HA! We'd be dead immediately. Feel sorry for the suckers in Vermont who might live.
It is not my area of expertise but the books and articles I've read in poli sci lately say it was very serious but not as serious as the U.S. propaganda.
Of course, now we know the Soviet Union's worries (valid ones) and strategy. It is easy to look back with hindsight and say it would not be the end of the world.
I consistently read that the U.S. moved missiles, aimed at the Soviet Union, into Turkey. JFK earlier decided to remove them. The Soviets were outraged that the missiles remained. Kennedy was shocked to find out the missiles were still in Turkey. Also, the Soviets studied Kennedy the man for years before he was elected. They saw a dilletante, playboy Senator who rarely showed up for work. His affairs with East German spies were well known to the Soviets. They figured he would cave at the slightest provocation. They were surprised. If Nixon were elected, there may not have been a stalemate. Kennedy was their favorite for president. Kennedy grew up quickly.