Inside Carnival cruise nightmare: Passenger describes deteriorating conditions

(CBS News) A four-day luxury cruise has turned into a week of misery.

An engine fire crippled the power supply of the Carnival Cruise Lines ship Triumph. Now, passengers say they're seeing disgusting conditions.

Cruise ship adrift in Gulf of Mexico for 3 days
Conditions worsen on damaged cruise ship

With two tug boats and a Coast Guard escort, the Triumph is slowly crawling towards Mobile, Ala. The ship is currently 200 miles south of the Alabama city. It's expected to dock around noon on Thursday. But for passengers and their anxious families, it can't happen soon enough. The concern now is keeping people on-board healthy and safe.

Nick Ware's mom Kimberly is one of 3,000 passengers stuck on-board. She's kept in touch via text messages and told her son she had to wait in line for hours just to get a burger.

Ware said, "Trash is piling up, food's cold, hard to get, long lines, pretty miserable. ... The people who did actually have meat on their burgers, it was cold and the remainder of the people once they ran out of the cooked meat. It was basically just onions and things like that on the sandwiches."

The nightmare started Sunday when an engine fire knocked out power leaving the ship drifting in the Gulf of Mexico. Since then, passengers have complained about everything from the sweltering heat to sewage running down cabin walls.

Passenger Donnell King described the scene: "People are sleeping in hallways. I mean there's just mattresses and people collected everywhere."

Carnival Cruise Lines apologized Tuesday and said Triumph has running water and most of its 23 public bathrooms are now working. Gerry Cahill, Carnival Cruise Lines president and chief executive officer, said, "Let me assure you that no one here from Carnival is happy about the conditions on board the ship. We're obviously very, very sorry about what is taking place."

The tugboats are hauling the 900-feet-long vessel at about six miles per hour -- one third the normal speed. Coast Guard Cmdr. Greg Magee is monitoring the operation. He told CBS News over the phone, "One of the big challenges we have right now is that it's a very large ship with a lot of sail area, so it's a difficult vessel to tow."

The Coast Guard and the National Transportation Safety Board have also launched an investigation into the fire that started it all.

Ware said, "I absolutely think it should be investigated. I think if you have an event like this it strands that many people out there and it's handled in this manner. Something needs to be done. This needs to be prevented."

Once the ship docks, Carnival has to get 3,000 passengers back home, so they've rented 1,500 hotel rooms in New Orleans and Mobile for the night, and chartered 20 flights to take passengers to Houston the next day.

For Anna Werner's full report, watch the video in the player above.