HAVANA – Tropical Storm Isaac pushed into Cuba on Saturday after sweeping across Haiti’s southern peninsula, where it caused flooding and at least three deaths, adding to the misery of a poor nation still trying to recover from the terrible 2010 earthquake.

Isaac’s center made landfall just before midday near the far-eastern tip of Cuba, downing trees and power lines. In the picturesque city of Baracoa, the storm surge flooded the seaside Malecon and a block inland, destroying two homes.

Forecasters said Isaac poses a threat to Florida on Monday and Tuesday, just as the Republican Party gathers for its national convention in Tampa. It could eventually hit the Florida Panhandle as a Category 2 hurricane with winds of nearly 100 mph.

Florida Gov. Rick Scott declared a state of emergency, officials urged vacationers to leave the Florida Keys and the U.S. National Hurricane Center said a hurricane warning was in effect there, as well as for the west coast of Florida from Bonita Beach south to Ocean Reef and for Florida Bay.

At least three people were reported dead in Haiti. A woman and a child died in the town of Souvenance, Sen. Francisco Delacruz told a local radio station. A 10-year-old girl died in Thomazeau when a wall fell on her, said Marie Alta Jean-Baptiste, director of Haiti’s Civil Protection Office.

She said as many as 5,000 people were evacuated because of flooding.

Many, however, stayed and suffered.

The Grive River overflowed north of Port-au-Prince, sending chocolate-brown water spilling through the sprawling shantytown of Cite Soleil, where many people grabbed what possessions they could and carried them on their heads, wading through waist-deep water.

“From last night, we’re in misery,” said Cite Soleil resident Jean-Gymar Joseph. “All our children are sleeping in the mud, in the rain.”

Scores of tents in quake settlements collapsed, including more than 50 in Cite Soleil.

About 300 homes in Cite Soleil lost their roofs or were flooded 3 feet deep, according to Rachel Brumbaugh, operation manager for the U.S. nonprofit group World Vision.

Doctors Without Borders said it anticipated a spike in cholera cases due to flooding.

The international airport reopened by the afternoon but there was still extensive flooding throughout Port-au-Prince after 24 hours of steady rain.

Isaac was centered about 40 miles north of Guantanamo Bay, Cuba, with maximum sustained winds of 60 mph, the Hurricane Center reported. It was moving northwest at 17 mph.

Tropical storm-force winds extended nearly 205 miles from the center, giving Isaac a broad sweep as it passed.

Forecasters said the storm was likely to march up the Gulf of Mexico, off Florida’s west coast, as a hurricane on Monday, just as the Republican National Convention is scheduled to start.