if you're in the city in which you were born, you should be able to get a copy lickety-split.
You don't need it to cruise, but if you break a leg and can't get back on the ship, you'll need to prove citizenship to get back in the country.
For some people, just easier to have what you need than it is to have to go through all the crap.
Actually, you DO need it to cruise (or something similar). What you don't need (for a closed loop cruise) is a passport.
Here's the information:
U.S. citizens on closed-loop cruises (cruises that begin and end at the same port in the U.S.) will be able to enter or depart the country with proof of citizenship, such as a government-issued birth certificate and laminated government issued picture ID, denoting photo, name and date of birth. A U.S. citizen under the age of 16 will be able to present either an original, notarized or certified copy of his or her birth certificate, a Consular Report of Birth Abroad issues by DOS, or Certificate of Naturalization issued by U.S. Citizenship and Immigration Services.
http://www.getyouhome.gov/html/lang_eng/eng_sa.html