Carnival Cruise Lines said it will take 4 to 5 hours to disembark the stricken Carnival Triumph after the ship docks in Mobile, probably some time Thursday evening.
The cruise line said it plans to disembark children and disabled passengers first. The lack of power means few elevators are working, complicating the process.
Carnival plans to organize crew members into a baggage brigade to hand-pass luggage in stairwells.
Earlier today, a tow line from one of the four tugs hauling Triumph into port snapped. The line was replaced and the ship entered an approach channel about an hour later.
Triumph is the largest cruise ship ever to dock in Mobile. The city's disused cruise terminal, built for Carnival but abandoned because of weak demand, is getting an emergency makeover to handle Triumph's 3,143 passengers.
Customs and Border Protection personnel were tendered to the ship before it reached port to begin the process of clearing passengers in advance of arrival.
Local harbor pilots have also boarded to guide the ship to a successful docking.
Earlier in the day, Carnival helicoptered more provisions and another generator onto Triumph to improve hotel services.
Carnival said its staff has taken more than 7,000 phone calls from guests' family members and friends.
The plight of passengers was the lead story on NBC Nightly News, which showed the open decks of the ship festooned with makeshift white tents.
Follow Tom Stieghorst on Twitter @tstravelweekly.