PORT-AU-PRINCE, Haiti — Tropical Storm Isaac swept across Haiti’s southern peninsula early Saturday, dousing a capital city prone to flooding and areas of the poor nation still trying to recover from the terrible 2010 earthquake.

The storm was heading toward eastern Cuba and forecasters said it poses a threat to Florida just as the Republican Party gathers for its national convention in Tampa. The U.S. National Hurricane Center in Miami said a hurricane warning is in effect for the Florida Keys and for the west coast of Florida.

Rocks, mud and other debris littered the streets of Port-au-Prince on Saturday morning and the city was on high alert for potential flooding. But the worst of the storm has hit far from the capital.

At least two people died, a woman and a child, in the town of Souvenance, Sen. Francisco Delacruz told a radio station.

Forecasters said Isaac could dump as much as eight to 12 inches and even up to 20 inches on Hispaniola, which is shared by Haiti and the Dominican Republic, as well as produce a storm surge of up to 3 feet.

Government and international aid groups in Haiti’s capital had been prepared to evacuate several thousand people from settlement camps that sprang up after the 2010 earthquake.