The ship is docked in port at Philipsburg, St. Maarten.
In an email to CNN on Thursday, passenger Jonath Evans of Reidsville, North Carolina, said "The
Passenger Gregg Stark told CNN, "There's human waste all over the floor in some of the bathrooms and they're overflowing -- and in the state rooms."
The Dream has not lost power, Carnival wrote on its Facebook page: The ship has full power but is still at dock while personnel continue to work on the technical issue."
The Dream left Port Canaveral, Florida on Saturday, for a seven-day cruise.
While the ship, with room for more than 3,500 passengers and 1,300 crew, is in port, the limited power and overflowing waste call to mind the Carnival Triumph, which was left adrift in the Gulf of Mexico last month after an engine room fire.
It took five days to tow the enormous vessel back to port, and its passengers were stuck on a ship without power and very few working toilets. Carnival Corporation is now facing a class-action lawsuit filed by Triumph passengers.