(CNN) -- Not yet a hurricane, Tropical Storm Isaac has already delivered shock waves from the Caribbean to Florida, postponing terror trial hearings in Cuba and posing a potential threat to next week's GOP convention in Tampa.
Isaac's path remains uncertain, but some computer models show the storm slicing its way up Florida's peninsula. Others send it farther west, into the Gulf of Mexico.
Officials are taking the threat seriously.
Gov. Rick Scott will talk about Florida's preparations for the storm at a media briefing Thursday morning at the State Emergency Operations Center in Tallahassee.
Tampa Mayor Bob Buckhorn said his city is prepared for the 50,000 people headed to his city for the Republican National Convention, which starts Monday.
The latest forecast map from the National Hurricane Center in Miami shows Isaac passing near south Florida late Sunday as a Category 1 hurricane and northwest of Tampa by Monday evening.
"We have contingency plan after contingency plan," Buckhorn said. "We are ready in the event that it happens. I don't think it's going to be a factor in this particular convention. But we are prepared in the event that it is."
Convention spokesman Kyle Downey said the situation is being monitored "very closely."
Possibly complicating matters, the convention site -- The Tampa Bay Times Forum -- is mandatory evacuation zone once storms reach 96 mph or a Category 2 hurricane, according to the Hillsborough County Hurricane Guide. The current forecast doesn't have Isaac reaching that status.
At the U.S. naval base at Guantanamo Bay, Cuba, officials canceled the pretrial arguments scheduled to get under way in the trial of Khalid Sheikh Mohammed and four others.
Mohammed -- who has been held since 2006 -- is facing charges related to the September 11, 2001, terrorist attacks.
Pentagon officials said all court events at Guantanamo were canceled because of the potential hurricane. All detainees have been moved to buildings that can withstand such a storm, and those who flew in for the hearing went back home.
Early Thursday, Isaac was about 265 miles southeast of San Juan, Puerto Rico, with maximum sustained winds of 45 mph, the hurricane center said.
Officials in the Dominican Republic issued a hurricane warning along the nation's southern coast. The nation's center of emergency operations put 18 provinces under red alert as the storm advances.
Tropical storm warnings covered much of the Leeward Islands, as well as Puerto Rico and the Virgin Islands.
"Some strengthening is forecast during the next 48 hours, and Isaac could become a hurricane on Friday," the hurricane center said.
Isaac could bring 4 to 8 inches of rain over the Northern Windward Islands and the Leeward Islands, the center said, and up to 6 inches of rain in Puerto Rico and the Virgin Islands.
On the island of Hispaniola, home to the Dominican Republic and Haiti, 8 to 12 inches of rain, with maximum amounts of 20 inches, are possible, the center said.
"These rains could cause life-threatening flash floods and mud slides," according to forecasters.
Puerto Rico Gov. Luis Fortuno said the U.S. commonwealth has as many as 433 shelters ready to be activated by local mayors as the storm approaches.
Aid organizations were keeping an eye on Haiti, where hundreds of thousands still live in camps after the deadly 2010 earthquake.
According to the U.N. High Commissioner for Refugees, 421,000 people are in camps in and around Port-au-Prince.
Isaac could be the first significant storm to hit Haiti since the devastating earthquake. Tropical Storm Emily threatened in 2011, but it weakened before hitting western Haiti.
The forecast map shows Isaac crossing the nation as a tropical storm with winds under 74 mph.
"We watch those storms every single time they come near because Haiti is so vulnerable," said Amy Parodi, a spokeswoman for the Christian humanitarian organization World Vision.
The agency has met with the government in previous summers to discuss contingency plans for major storms, and pre-positioned relief items are available, she said.