It's probably going to be much less of a deal for people with passports than it is going to be for those without.

As ABC is reporting

Some of the passengers likely do not have passports, an issue that could slow down re-entry to the U.S. via flight. Passengers on a "closed loop" cruise -- that is, a cruise that begins and ends in the same U.S. port -- do not need a passport even if their ship calls on ports outside the country. However, a passport is required for all passengers returning to the U.S. from outside the country via air.