Forecasters said Ernesto could grow back into a hurricane in the warm waters off Cuba and come ashore in South Florida as early as Tuesday night, exactly one year after Hurricane Katrina pummeled the Gulf Coast.
It would be the first hurricane to hit the United States this year.
In all, eight hurricanes have struck or bruised Florida in just the last two years, reports CBS News correspondent Cynthia Bowers, and Ernesto could dump anywhere from 8 to 20 inches of rain and cause significant coastal flooding.
"Make sure you have the supplies for the 72 hours after the storm," Gov. Jeb Bush warned people in Tallahassee, a day after declaring a state of emergency for all Florida. "A hurricane's a hurricane, and it has a devastation we've already seen. All you have to do is rewind to last year and see."
CBS News hurricane expert Bryan Norcross says that even though Ernesto is still a tropical storm, people in south Florida are planning for a hurricane.
Pedro Ballesteros, 40, carried two new 10-gallon gas tanks out of a Home Depot for his home generator.
"Every year we prepare a little more because we're learning from our past ordeals," he said. "I'm taking care of everything that's important — flashlights, batteries, gasoline."
The storm's path and intensity were far from clear. Forecasters said there was a 10 percent chance of hurricane-force winds striking South Florida and a 60 percent chance of tropical storm-force winds by Thursday.
About 400 miles of the state's densely populated Atlantic coast and the Keys — including the Miami, Fort Lauderdale, Palm Beach and Cape Canaveral areas — were under a hurricane watch.
At 2 p.m. EDT, the fifth named storm of the hurricane season had winds of 40 mph, 1 mph above the minimum to be a tropical storm and down from a hurricane-strength 75 mph on Sunday, the National Hurricane Center said. It was centered over Cuba, about 450 miles southeast of Key West, and was moving northwest at 10 mph.
Over the weekend, Ernesto became the first hurricane of the Atlantic season and lashed the Dominican Republic and Haiti. One person was reported killed along Haiti's southern coast.
There were no immediate reports of any damage or injuries in Cuba. The government regularly undertakes mass evacuations before tropical storms and hurricanes. This time, Cubans moved cattle to higher ground, tourists were evacuated from hotels, and baseball games were rescheduled for earlier in the day in Havana.
Forecaster Richard Knabb at the hurricane center in Miami urged people not to become complacent. "Just because the system is not a hurricane now, doesn't mean it can't be a hurricane later," he said.
In the Keys, visitors were ordered out, and authorities planned to evacuate sick and elderly people to Miami. Mobile home residents in the Keys were also urged to clear out. Miami-Dade County opened a shelter for people from the Keys.
Some Keys residents and business owners put plywood over windows or installed hurricane shutters as tourists struggled to get flights out.
As of midafternoon, no large-scale evacuations were ordered on the Florida mainland.
NASA dropped plans to launch the space shuttle on Tuesday and was prepared to roll Atlantis back to its giant hangar if necessary. Cruise ship companies diverted several liners to avoid the storm.
Many Florida residents rushed to stores to gather supplies and fill prescriptions. Motorists had to wait up to an hour and a half at several gas stations across South Florida.
Adrian Scarani, manager of a Marathon service station on a busy intersection in Miami-Dade County, ran out of regular gasoline. "It was crazy here this morning," he said.
Kathleen Campos shopped for food and water at a Winn-Dixie in Miami and was also worried about getting enough cash, which might be hard to find after a storm if the electricity is knocked out.
Counties along the coast offered sandbags and got ready to distribute ice and water. Broward and Miami-Dade counties canceled school on Tuesday so that students would not get caught in the storm on their way home.
James Krie, 44, a Key West resident and general contractor, seemed unconcerned about the brewing storm. He acknowledged that outsiders might not understand.
"I feel like they look at us and say, `You dummies live down there,"' he said.