http://travel.state.gov/content/passports/english/passports/information/do-i-need.html
"*"Closed-Loop" Cruises: If you are a U.S. citizen, and you board a cruise ship at a U.S. port, travel only within the Western Hemisphere, and return to the same U.S. port on the same ship, you may present government-issued photo identification, along with proof of citizenship (an original or certified copy of your birth certificate, a Consular report of Birth Abroad, or a Certificate of Naturalization). Please be aware that you may still be required to present a passport to enter the foreign countries your cruise ship is visiting. Check with your cruise line to ensure you have the appropriate documents."

I would strongly recommend traveling under a passport though. It would not be fun to have a medical emergency and then find yourself stuck in Mexico without a passport.