The 4,500 passengers and crew on board the Carnival Splendor, low on food and without air conditioning or hot water, are having to eat canned crab meat and Spam dropped in by helicopters, and their plight is expected to continue until the ship finally reaches port early on Friday.
What began as a seven-day cruise to the picturesque Mexican Riviera turned into a nightmare on Monday when an engine room fire cut power to the 952ft vessel and set it adrift off Mexico's Pacific coast.
No-one was hurt in the fire and by Tuesday, US Navy helicopters had started ferrying supplies to the stricken vessel.
The tugboats were originally set to take the Splendor to the Mexican coastal city of Ensenada, but Carnival Cruise Lines has now changed its plans and is attempting to have it towed to San Diego, where hotel and flight arrangements would await the passengers.
But if the process moves too slowly, the ship might still be taken to Ensenada, the company said.
US Coast Guard petty officer Kevin Metcalf said the tugs and a coastguard cutter escort would have to move slowly because the ship is so big.
The Splendor, which left Long Beach, California, on Sunday, was about 200 miles south of San Diego at the time of the engine fire. It began drifting about 55 miles offshore.
The 3,299 passengers and 1,167 crew members were not hurt and the fire was put out in the generator's compartment, but the ship now has no air conditioning, hot water, mobile phone or internet service.
On Tuesday, US sailors loaded cargo planes with supplies for the stranded passengers. The Coast Guard deployed aircraft and ships, the Mexican Navy is assisting and the US Navy diverted the aircraft carrier USS Ronald Reagan from training manoeuvres to help.