Ivan has killed at least 60 people as it has torn a path of destruction across the Caribbean, and was headed next for a and the southeastern United States.
Officials in the Florida Keys said they were "cautiously optimistic" Hurricane Ivan might spare the island chain its worst punishment.
Still, the National Hurricane Center issued a tropical storm watch Sunday morning for the lower third of the 120-mile island chain, from below Marathon through Key West and the Dry Tortugas. A watch means tropical storm conditions are possible within 36 hours.
The storm initially was projected to hit the Keys directly, but it unexpectedly wobbled and lurched west early Saturday, bringing hope to weary Floridians who already have suffered through two other hurricanes in less than a month.
"From a psychological standpoint, it feels better, but from a meteorological standpoint we're not out of the woods yet," said Matt Strahan, a National Weather Service meteorologist in Key West.
Hurricanes Frances and Charlie killed more than 50 people in Florida. Thousands remain in shelters, their lives scattered like trash, their homes now giant heaps.
At the very least, Ivan is predicted to bring more heavy rains to homes with nothing but tarps, and if it plows ashore in the Panhandle, like a weaker Francis did Monday morning, an already soggy ground will shed water like a ducks' feathers, right into already-flooded homes, reports CBS News Correspondent Lee Cowen.
The hurricane, which grew to the most powerful Category 5 scale with 165 mph winds Saturday, lost some strength before it began tearing into the Cayman Islands, a popular scuba diving destination and banking center that benefits from strict building codes.
"It's as bad as it can possibly get," Justin Uzzell, 35, said by telephone from his fifth-floor refuge in Grand Cayman. "It's a horizontal blizzard," he said, "The air is just foam."
Emergency officials said residents from all parts of the island were reporting roofs blown off and flooded homes as Ivan's shrieking winds and driving rain approached Grand Cayman, the largest of three islands that comprise the British territory of 45,000 people.
The airport runway was flooded and trees were wrenched from their roots, including a giant Cayman mahogany next to the government headquarters in downtown George Town. Radio Cayman went off the air, then resumed broadcasts.
Though there were no immediate reports of injuries in the Cayman Islands, the death toll elsewhere rose as hospital officials in Jamaica reported four more deaths, for a total of 15 there. At least 34 were killed in Grenada, where the hurricane left widespread destruction. Scattered deaths occurred on other islands and in Venezuela.
Ivan was projected to make a direct hit on western Cuba on Monday before moving into the Gulf of Mexico on Tuesday, nearing the Florida Keys and parts of Florida's Gulf coast.
The storm raked Jamaica's southern coast on Saturday, never directly hitting the island but pounding it with monstrous waves and torrential rains.
Some people were stranded in flooded homes in the north-central parish of St. Anne near Ocho Rios, and emergency officials said they were trying to get a helicopter to evacuate people because roads were impassible.
The storm could dump up to 1 foot of rain, possibly causing flash floods and mud slides, according to the Hurricane Center. Its 150 mph winds were just one mile below a Category 5 storm.
The Cayman Islands' National Hurricane Committee urged people to stay indoors as sheets of rain fell near horizontally in the whipping winds.
The Cayman Islands have strong building codes that are strictly enforced, but Ivan's raging winds were shaking the reinforced concrete building housing the hurricane committee at Owen Roberts International Airport, and flooding forced officials to evacuate the ground floor.
"It's constructed to withstand this kind of thing, so that makes you concerned for buildings that are not as well constructed," Emanuel said.
Ambulances and other emergency vehicles were three feet under water, he said.
Flying debris tore shutters off some shelters and bashed open the door of one, which had to be propped closed. At least one beach resort lost its boat dock.
Hundreds of people left the Caymans chartered flights before the hurricane came and most of the 150 residents of Little Cayman were brought to the big island before the storm.
Officials reported 3,000 people had filled all shelters on Grand Cayman and about 750 in Cayman Brac island were in shelters.
Electricity and water service was cut before the storm to prevent electrocutions and damage to plants.
In Cuba, President Fidel Castro said his government had mobilized to save lives and property.
"This country is prepared to face this hurricane," Castro said Saturday night. Ivan is the most powerful storm to threaten the country since the 1959 revolution that brought Castro to power.
The threatened area includes densely populated Havana, where traffic was light Sunday morning as most took shelter.
About 800,000 people across the island of 11.2 million had been evacuated by Sunday morning, with most seeking refuge with relatives, the official Prensa Latina news agency reported.
Kingston's airport remained closed because the Palisadoes Highway leading to it was blocked by dunes of sand up to five feet high. Bulldozers were clearing the sand Sunday.
Jamaican police killed two alleged looters and four officers were wounded in shootouts with armed looters, officials said.
Ivan also killed five people in Venezuela, one in Tobago, one in Barbados, and four children in the Dominican Republic.
The fourth major hurricane of the Atlantic season, Ivan damaged dozens of homes in Barbados, St. Lucia and St. Vincent on Tuesday before making a direct hit on Grenada, which was left a wasteland of flattened houses. It also destroying nearly 100 houses and damaged hundreds more in impoverished Haiti.