Story highlights The first of 2 tugboats that will tow the ship to Alabama arrives, Carnival says

The cruise ship will go to the U.S., not Mexico, due to currents and "simpler re-entry"

An engine room fire disabled the ship; passengers report many issues aboard

A Carnival spokesman admits problems on ship but points to progress

Passengers on a Carnival cruise ship drifting in the Gulf of Mexico aren't getting the vacation they expected -- sleeping on its decks, making do with a few working toilets, and doing what they can to get food -- all due to a weekend engine fire left the vessel dead in the water.

The Carnival Triumph was about 150 miles off the coast of Mexico's Yucatan Peninsula, heading back Sunday morning to Galveston, Texas -- where it had departed Thursday on a four-day trip -- when a fire broke out in an engine room, according to Carnival Cruise Lines.

The ship's automatic fire extinguishing system kicked in and soon contained the flames, and no injuries were reported, Carnival reported.

Yet this fire left the ship -- and its 3,143 passengers and 1,086 crew members -- adrift without propulsion, the cruise line said, halting its trip back to port.

The first of two tugboats that will tow the ship to Mobile, Alabama, arrived on Monday evening, the cruise line said in a statement. The ship should arrive in the Gulf city some time Thursday.

Not being able to sail, though, is just one of the problems. Issues with running water, scarce electricity and more contributed to headaches big and small, according to passengers and their loved ones.

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Toby Barlow's wife Ann told him there was "sewage running down the walls and floors" with passengers being asked to defecate in bags and urinate in showers due to a lack of functioning toilets. Food lines ran 3½ hours long and some, like herself, slept outside to keep cool.

"Elderly and handicap(ped people) are struggling," she texted her husband. "The smells are gross."

Brent Nutt said his wife, Bethany -- who is on board, and whom he talked to Sunday -- reported similar problems.

"She said they had no power, no running water, and she said she hadn't been able to eat anything yet. Then you call the Carnival phone number for families, and they tell you that everything is all right," Nutt told CNN.

Posts to CruiseCritic.com , which bills itself as an "interactive community of avid and first-time cruisers," documented similar issues with power and more. Some posts, though, were more light-hearted.

"They are all fine," wrote one woman, whose sister is on board. "Said they are still having fun and gave me the task to call her boss who seems to think I was lying."

Carnival spokesman Vance Gulliksen acknowledged issues, while noting the cruise line's efforts to address the situation.

Some people are camping out on the decks because some cabins don't have air conditioning, he said Monday evening.

And Gulliksen pointed to recent progress. For instance, "we have restored toilets in some public areas and cabins;" there is running water for showers, even if it's cold; and some elevators are working.

As for the food situation, he said the Triumph's poolside restaurant has "limited food service" and meals have been brought aboard from two other Carnival ships. Earlier Monday, the cruise line said in a statement that there was hot coffee available, among other options.

"All our guests are safe, and we're doing everything we can to make them as comfortable as possible," Carnival CEO Gerry Cahill said in a statement issued at 8:30 p.m. ET Monday. "We're terribly sorry for the inconvenience, discomfort and frustration our guests are feeling."

Besides the two Carnival vessels that have come to transfer supplies -- and, in one case, take on a passenger with a pre-existing medical condition, said Gulliksen -- the U.S. Coast Guard cutter Vigorous is on-site to aid the stranded ship.

"It's in deep water and not near any hazards to navigation," said Greg Magee, the commander of the Vigorous.

The ship was initially expected to be towed into the northern Yucatan port of Progreso, Mexico. But the ship had already drifted about 90 miles north due to strong currents by Monday night, prompting the decision to instead move the Triumph to Mobile.

Carnival said Mobile and Progreso were then roughly equidistant, adding that strong currents toward the Alabama shore and a "simpler re-entry" -- especially for the 900 passengers without passports -- also drove the decision to head to the U.S. coast.

After being towed to port, those aboard the Carnival Triumph will be flown home at no cost to them, the cruise line said. They will also get a full refund, credit that can be used toward a future trip and reimbursement for all expenses, except casino and gift shop purchases, for their current trip.

The vessel's next two departures, scheduled for Monday and Saturday, have been canceled. Those slated to be on those trips will get full refunds and discounts toward future cruises, the cruise line said.

Family and friends of those on board may call 888-290-5095 or 305-406-5534 for information.

Throughout the ordeal, Barlow said his wife Ann has kept her sense of humor despite being stranded.

"I joked with her that I got the raw end of the deal. I was stuck in Texas with all (the) kids going to watch midget wrestling while she was on a cruise this weekend with her girlfriends," he said. "When I talked to her (Sunday) night, I reminded her maybe I got the better end of the deal," he said.