Fun2cruise is right, it is a risk game and the monies do not compare to the risk of being left in a foreign port to fly home.
Those airport authorities will be wanting a passport and ( if they let you on board) your friendly American welcome home Airport security and immigration will be wanting to see your passport as well.
Best case, the foreign port folks might deport you sans passport except you walk into fun on arrival or you have to request an emergency passport from the American Consulate which is not on every Island.
In all probability you will not have a problem as long as you get back on board in time and are a model passenger so you are not removed from the ship.
Me, I'm too cautious, I go for passport
Celebrity Infinity-1, Dawn Princess-1, Sea Princess-2, Golden Princess-2, HA Maasdam-1, SS Cavina-1
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