Forecasters expect Isaac to move over Cuba today and become a hurricane tomorrow.
A hurricane warning is in effect for the Florida Keys including the Dry Tortugas, the west coast of Florida from Bonita Beach southward, and Florida Bay.
A hurricane watch is in effect for the Florida east coast from Golden Beach southward, Andros Island in the Bahamas and Haiti.
A tropical storm warning is in effect for parts of the Florida east coast from Jupiter Inlet southward, Lake Okeechobee, parts of Cuba, the Bahamas, and the Turks and Caicos Islands. A tropical storm watch is in effect for Florida's east coast north of Jupiter Inlet to Sebastian Inlet.
Though Isaac has weakened somewhat, it is packing heavy rain and 60-mph winds to Haiti and the Dominican Republic. It could trigger mudslides. Parts of Cuba have declared a state of emergency.
CBS News hurricane consultant David Bernard reports there is great concern in South Florida and the Keys - and for the rest of the peninsula as well.
Early Saturday morning the storm was 95 miles southeast of Guantanamo. Bernard says the future track of Isaac brings it to a category 1 on Sunday afternoon as it approaches South Florida and the Keys, with the possibility of becoming even stronger than that.
By Monday night or Tuesday morning, it will make its closest approach to the west coast of Florida including the Tampa area, with a second landfall possible as Wednesday or Thursday.
Organizers of next week's Republican National Convention in Tampa say they are monitoring the storm. Some 70,000 delegates, journalists and protesters are expected, and Florida Gov. Rick Scott said there are no plans to cancel the convention.