(ABCNEWS)-- The ordeal of the disabled Carnival Triumph cruise ship carrying 4,000 passengers and crew appears to be almost over, with relatives waving at passengers on board as the ship reached port in Mobile, Ala.
The ship arrived around 9:30 p.m. local time (10:30 p.m. ET).
Once the ship is secured, passengers are expected to be able to begin disembarking within 15 to 30 minutes, a Carnival official said.
"Inside the terminal, there's also warm food available," said the Carnival official, Terry Thornton, senior vice president of marketing for the cruise line. "There are blankets, there are cell phones and refreshments available for the guests that need that or want that assistance.
"We're focused completely tonight on our guests and getting them on their journey home," Thornton added.
It could take up to five more hours to get everybody off the huge ship.
"There are some limitations. We know that up front," Thornton said at an earlier news conference this afternoon. "The ship still does not have power. We only have one functioning elevator aboard."
Thornton said that anyone with special needs and children will be the first to get off the boat. He said the company's number one priority is to make the process as "quick, efficient and comfortable" for guests as possible.
"We're not anticipating any additional difficulties," he said.
The passengers were achingly close to port about noon today as the ship began to enter the channel and proceed to the cruise terminal. At 1 p.m., the lead tow boat had a tow gear break, so a spare tug boat that was on standby had to be sent in to replace it.
But once the second tug was in position and the lines were re-set, the towing resumed only briefly before the tow line snapped.
"We had to replace that tow line so the ship did not begin progressing back into the cruise terminal until 2 p.m.," Thornton said
Passengers desperate to get off the vessel waved at media helicopters that flew out to film the ship and passenger Rob Mowlam told ABCNews.com by phone today that most of the passengers on board were "really upbeat and positive."
Nevertheless, when he gets off Mowlam said, "I will probably flush the toilet 10 times just because I can."
Mowlam, 37, got married on board the Triumph Friday and said he and his wife, Stephanie Stevenson, 27, haven't yet thought of redoing the honeymoon other than to say, "It won't be a cruise."
Alabama State Port Authority Director Jimmy Lyons said that with powerless "dead ships" like the Triumph, it is usually safer to bring them in during daylight hours, but, "Once they make the initial effort to come into the channel, there's no turning back."
"There are issues regarding coming into the ship channel and docking at night because the ship has no power and there's safety issues there," Richard Tillman of the Mobile Bay Convention and Visitors Bureau told ABCNews.com.
When asked if the ship could be disembarked in the dark of night, Tillman said, "It is not advised. It would be very unusual."
Thornton denied the rumors that there was a fatality on the ship. He said that there was one illness early on, a dialysis patient, but that passenger was removed from the vessel and transferred to a medical facility.
The U.S. Coast Guard is assisting now and there are multiple generators on board. And customs officials will board the ship while it is being piloted to port to accelerate the embarkation, officials said.
After eight days at sea, many of them without power, the ship's owners have increased the compensation for what some on board are calling the vacation from hell.