PORT-AU-PRINCE -- Emerging from Haiti largely intact, Tropical Storm Isaac churned toward Cuba on Saturday on a path that made it a more serious hurricane threat for South Florida.

The National Hurricane Center placed the Florida Keys, South Miami-Dade and a portion of the Gulf Coast under a hurricane warning, with Isaac expected to approach Sunday as a 75- to 80-mph hurricane, veering across the Lower Keys and skirting the state’s southwestern tip. The rest of Miami-Dade was under a hurricane watch and tropical storm warnings and watches extended up the east coast to Sebastian.

At 8 a.m., the hurricane center reported that Isaac’s core had crossed southwestern Haiti and was in the Windward Passage, slightly weaker with 60 mph winds. But it was now on track for a relatively brief passage over Cuba that forecasters believe will give it more time to strengthen in the Florida Straits.

The large storm could produce from 6 to 10 inches of rain and powerful gusts across much of South Florida, with tropical storm force winds beginning to buffet the Keys Sunday and building to hurricane force. Squalls that drenched South Florida overnight Friday and Saturday morning weren’t part of Isaac but a hint of the dreary weather to come.

Overnight, Isaac became a more serious threat than emergency managers in South Florida had expected on Friday.

Monroe County has ordered schools and some offices closed but decided not to order a mandatory evacuation of tourists. In Miami-Dade, Mayor Carlos Gimenez and emergency managers on Friday urged residents to prepare but said that there were not yet plans to cancel school, close offices or shut down services.

“We don’t anticipate this to be like Hurricane Andrew,” Gimenez said on Friday.

In Haiti, damage reports were coming in from across the country -– and the heaviest rains in Isaac’s wake were still to come.

Marie-Alta Jean-Baptiste, head of Haiti’s disaster operations, said a 10-year-old girl died in Thomazeau, a community outside of Port-au-Prince. Also 3,000 persons were evacuated into shelters. In Port-au-Prince, trees and power lines are downed. Firefighters rushed to put out a church fire in the middle of the night. No one was injured, police said.

Government workers, including police, were forced to evacuate several camps in the middle of the storm as the howling winds ripped tents, and tore award corroded zinc walls of shacks. Unable to withstand Isaac, earthquake refugees in the Marassa tent village, who earlier in the day had refused to evacuate, called police for help shortly before 1 a.m.

Les Cayes, a flood-prone seaside town near the center of Isaac, seemed to have escaped the worst. But the city of Jacmel, in southeast Haiti, was without power.

"The rain isn’t that strong, and we don’t yet have winds. But Jacmel was hit a lot," said Roosevelt Guerrier, a government official in the southern region told The Miami Herald.

Disaster officials also rescued five people from a sinking fishing boat in Fort Liberte in Northeast Haiti, Some quake refugees continued to resist efforts to evacuate, fearing thieves would steal their meager possessions or, worse, the government and aid groups would use it as an opportunity to shut down camps.

“We’ve lived through this before. We’re not afraid,” said Lucien Pierre, 28, a mother of two including a 1-year-old, as she washed clothes outside her tent. “We’ll pray and watch.”