"Once they do get the tugs on scene they will start tow the Splendor back to port," said U.S. Coast Guard spokesman Patrick Montgomery. "It will take a while to get back to port. They'll probably do about three to four miles per hour so it'll be quite a lengthy journey."
There are 3,300 passengers and 1,200 crew members aboard the 113,000-ton vessel. They are stranded about 150 miles off the coast of San Diego.
An engine fire Monday morning forced passengers and crew members to move to the upper deck of the cruise ship to open air. It shut down air conditioning, hot-food service and telephones.
Cold water and flushing toilets had also been shut down, but they have since been restored. They also have emergency generators, bottled water, cold water and steady seas.
Carnival said no one was hurt, but there are reports of panic attacks on board.
"We know this has been an extremely trying situation, and we sincerely thank them for their patience," said Gerry Cahill, president and chief executive officer of Carnival Cruise Lines, in a statement.
The ship is stuck in open water about 55 miles west of Punta San Jacinto, Mexico. Passengers had boarded the Splendor and left from Long Beach on Sunday on the first leg of a seven-day Mexican Riviera cruise.
Officials had originally planned on towing the ship to Ensenada.
Planes are loading up with 35 pallets of supplies. The U.S.S. Ronald Reagan is expected to deliver more than 70,000 pounds of food.
When passengers return to Long Beach, Carnival will offer them full refunds and tickets for a future cruise.
"I'd say, 'No thank you.' That's like getting food poisoning at a restaurant, and then having them give you gift certificates to come back," said Jennifer Blair of Long Beach.
Those who have family members or friends on board the Carnival Splendor can call a hotline that has been set up at (888) 290-5095.
The Associated Press contributed to this story.