You should really get a passport for any travel outside the US regardless of how you're going. I know it's not required at this time to board a ship. The problem is, if you have a medical emergency in Ocho Rios do you really want them cutting out your apendix there? You will have no choice, there is no way without a passport to fly home for care. What if a family member were to die, God forbid but things happen. You won't be flying home from your cruise to join your family, you can't without a passport.
Just because the government doesn't require common sense doesn't mean we shouldn't use some when traveling. Everyone traveling outside the US should absolutely have a passport, even if you're walking across the border.