If its a closed loop cruise (beginning and ending in the U.S., which all the Fantasy ones are) you would be fine with a driver's license/state ID. Many recommend passports/a passport card as well, on the off chance of an illness or getting left behind on a port and having to fly home.
A driver's license/state ID is NOT sufficient. Even on a closed look sailing you would need at least a valid, certified, birth certificate.
I'd hate to see someone take the offer only to get turned away at port because they were given incorrect information.

Bill
the price without the discount was $11,600, so it was so tempting. I just need it to sell out quickly! 
DU tells me that if the offer requires payment in full and you call DCL directly, it cannot then be transferred to an agency...