MIAMI -- Hurricane Dorian powered toward Florida with increasing fury Friday, menacing its eastern coast with a potentially devastating direct hit while also giving indications it might just skirt up the U.S. coastline.

Forecasters warned no one is out of danger and Dorian could still wallop the state with "extremely dangerous" 140 mph winds and torrential rains late Monday or early Tuesday, with millions of people in the crosshairs along with Walt Disney World and President Donald Trump's Mar-a-Lago resort.

But some of the more reliable computer models predicted a turn northward having Dorian hug the coast, delivering a glancing blow, the National Hurricane Center said. Weather Underground meteorology director Jeff Masters said: "There is hope."

The faint, encouraging signs came at the end of a day in which Dorian seemed to get scarier with each forecast update. It strengthened into a Category 3 hurricane in the afternoon, and there were fears it could prove to be the most powerful hurricane to hit Florida's east coast in nearly 30 years.

Late Friday, the National Hurricane Center's projected new track showed Dorian hitting near Fort Pierce, some 70 miles north of Mar-a-Lago, then running along the coastline as it moved north. But forecasters cautioned the storm's track was still highly uncertain and even a small deviation could put Dorian offshore or well inland.

Trump declared a state of emergency in Florida and authorized the Federal Emergency Management Agency to coordinate disaster-relief efforts.

"This is big and is growing and it still has some time to get worse," Julio Vasquez said at a Miami fast-food joint next to a gas station that had run out of fuel. "No one knows what can really happen. This is serious."

As Dorian closed in, it played havoc with people's Labor Day weekend plans. Major airlines began allowing travelers to change their reservations without a fee. The big cruise lines began rerouting their ships. Disney World and the other resorts in Orlando found themselves in the storm's projected path.

Jessica Armesto and her 1-year-old daughter, Mila, had planned to have breakfast with Minnie Mouse, Donald Duck and Goofy at Disney World. Instead, Armesto decided to take shelter at her mother's hurricane-resistant house in Miami with its kitchen full of nonperishable foods.

"It felt like it was better to be safe than sorry, so we canceled our plans," she said.

Still, with Dorian days away and its track uncertain, Disney and other major resorts held off announcing any closings, and Florida authorities ordered no immediate mass evacuations.

"Sometimes if you evacuate too soon, you may evacuate into the path of the storm if it changes," Gov. Ron DeSantis said.

Homeowners and businesses rushed to cover their windows with plywood. Supermarkets ran out of bottled water, and long lines formed at gas stations, with fuel shortages reported in places. The governor said the Florida Highway Patrol would begin escorting fuel trucks to help them get past the lines of waiting motorists and replenish gas stations.

At a Publix supermarket in Cocoa Beach, Ed Ciecirski of the customer service department said the pharmacy was extra busy with people rushing to fill prescriptions. The grocery was rationing bottled water and had run out of dry ice.

"It's hairy," he said.

As of 4 p.m. Friday, Dorian was centered about 595 miles east of West Palm Beach with winds of 115 mph. It was moving northwest at an ever-slower 9 mph. Forecasters warned its slow movement could subject the state to a prolonged and destructive pummeling from wind, storm surge and heavy rain.

Coastal areas could get 6 to 12 inches of rain, with 18 inches in some places, triggering life-threatening flash floods, the hurricane center said. FEMA official Jeff Byard said Dorian is likely to "create a lot of havoc" for roads, power and other infrastructure.

Also imperiled were the Bahamas, where canned food and bottled water were disappearing quickly and the sound of hammering echoed across the islands as people boarded up their homes. Dorian was expected to hit by Sunday with the potential for life-threatening storm surge possibly raising water levels 15 feet above normal.

"Do not be foolish and try to brave out this hurricane," Prime Minister Hubert Minnis said. "The price you may pay for not evacuating is your life."

Florida's governor urged nursing homes to take precautions to prevent tragedies such as the one during Hurricane Irma two years ago, when the storm knocked out the air conditioning at a facility in Hollywood and 12 patients died in the sweltering heat. Four employees of the home were charged with manslaughter earlier this week.

DeSantis said the timely message from those arrests is: "It's your responsibility to make sure you have a plan in place to protect those folks."

At NASA's Kennedy Space Center in Cape Canaveral, NASA moved a 380-foot-high mobile launch platform to the safety of the colossal Vehicle Assembly Building, built to withstand 125 mph wind. The launcher is for the mega rocket NASA is developing to take astronauts to the moon.