MIAMI – Tropical Storm Ernesto’s leading edge drenched Miami and the rest of southern Florida on Tuesday as it steamed toward the Sunshine State with a potential for more than a foot of rain. But forecasters said there was only an outside chance it would strengthen into a hurricane.

Residents took no chances, though, mindful of the seven hurricanes that have hit the state since 2004 and Katrina, which struck New Orleans exactly one year ago.

“I don’t think it’s going to be too big, but you never know,”‘ said Frankel Herad as he removed brightly colored African dresses from the walls of his store in Miami’s Little Haiti neighborhood.

By late afternoon, Ernesto had top winds of 45 mph. And there was only a “remote possibility” it could become a hurricane with winds of 74 mph or greater before crossing over Florida overnight, the National Hurricane Center said.

“The storm has not been strengthening,” said Max Mayfield, the center’s director. “That window for it strengthening into a hurricane is definitely diminishing.”

Forecasters expected 5 to 15 inches of rain, which could flood streets and homes. Residents in flood-prone areas filled thousands of sandbags in anticipation of high water.

Ernesto, briefly a hurricane Sunday, lost much of its punch crossing mountainous eastern Cuba. The storm was expected to move up the middle of the state and over the northeastern coast by early Thursday before churning into the Atlantic Ocean, where it could regain hurricane status before hitting Georgia or the Carolinas.

Florida Gov. Jeb Bush, joined by Homeland Security Secretary Michael Chertoff, said the state was ready to respond to any problems with 500 National Guardsmen and another 500 state law enforcement officers.

“This does not look like a catastrophic event, but we always want to be ready,” said Chertoff, who had just come from the Katrina anniversary events in Louisiana and Mississippi.

NASA scrubbed Tuesday’s launch of Atlantis. The space agency began moving the shuttle back to its hangar to protect it from the storm, then reversed course later in the day when forecasters predicted winds would not be as severe as initially feared.

At 5 p.m. EDT, Ernesto was centered over warm open water in the Florida Straits, about 105 miles south of Miami. It was moving northwest at about 13 mph.

Across populous South Florida, residents scurried to make last-minute preparations. Most schools were closed, and lines formed early at groceries, gas stations, pharmacies and hardware stores.

Officials repeatedly urged people to have enough supplies for 72 hours, especially given the likelihood of power outages.

In Davie, Pedro Concepcion was about to leave his mobile home to get supplies, including wood to board up the windows and a tarp for his roof.

“Last year we had a lot of damage, so we want to be prepared. We still have some damage to windows,” he said.

Officials in the Miami-Dade and Fort Lauderdale areas urged mobile home residents to evacuate, though not all did so.

By late afternoon, there were more than a thousand people at shelters in Broward and Miami-Dade counties. Latosha Mikell reluctantly brought her 9-month-old son to a Miami shelter.

“There is no privacy here,” she said. “There is no bedding, and there are a lot of people just sleeping on the floor.”

Damage from 2004 and 2005 hurricanes continues to plague many residents, with thousands still awaiting roof repairs.

In Miami, 49-year-old Luckner Senatus prepared to move his family to their nearby church. His neat beige bungalow was still covered with a blue tarp, with yellow water stains on the walls. He was still waiting for a contractor to fix his roof.

“They called last night to say maybe next week they will begin work,” said Senatus, shaking his head. “We can’t stay here tonight. We are all going to have to leave.”

In the laid-back Florida Keys, many residents took the approaching storm in stride. Adam Bradford, a construction foreman from Marathon, helped a friend place shutters over the front windows at Dot’s Tattoos and Ranee’s Body Piercings. “You got to get everything ready, make sure it works,” he said.