Ike roared onto the island on Sunday after destroying houses and crops on low-lying islands, and worsening floods in Haiti that have already killed more than 300 people.
With Ike forecast to sweep the length of Cuba and possibly hit Havana head-on, CBS News producer Portia Siegelbaum reported that at least 1 million Cubans had been evacuated to shelters or higher ground.
"We are preparing for a strong hit," Cuban Vice President Carlos Lage told state television.
To the north, residents of the Florida Keys fled up a narrow highway, fearful that the "extremely dangerous" hurricane could hit them Tuesday. A tropical storm warning is now posted in the Florida Keys.
As of 11:00 a.m. EDT, Ike's sustained winds decreased slightly to near 100 miles per hour with higher gusts. The storm is centered about 290 miles east-southeast of Havana, and is moving to the west near 14 mph.
At least 58 people died as Ike's winds and rain swept Haiti Sunday - and officials found three more bodies from a previous storm - raising the nation's death toll from four tropical storms in less than a month to 319. It was too early to know of deaths on other islands where the most powerful winds were still blowing.
Ike's center hit the Bahamas' Great Inagua island, where the roofs of its two shelters both sprung leaks under the 135 mph winds. As the storm passed, people inside peeked through windows at toppled trees and houses stripped of their roofs.
"It's nasty. I can't remember getting hit like this," reserve police officer Henry Nixon said from inside a shelter holding about 85 people.
Todd Kimberlain, a meteorologist at the U.S. National Hurricane Center, said Ike reached land in eastern Cuba late Sunday night and was expected to remain over the island until Tuesday.
Siegelbaum reported late Sunday that official estimates put the number of homes destroyed in Guantanamo province at 80. "After watching footage from there, it's clear that many, many more will be leveled or severely damaged," she said.
The hurricane center predicted Ike's eye could hit Havana, the capital of 2 million people with many vulnerable old buildings, by Monday night.
State television broadcast images of the first damage in Cuba, showing a storm surge washing over coastal homes in the easternmost city of Bayamo. It reported that dozens of dwellings were damaged beyond repair.
"These storms have a mind of their own," Florida Gov. Charlie Crist said as tourists and then residents evacuated the Keys along a narrow highway.
In Louisiana, Gov. Bobby Jindal and New Orleans Mayor Ray Nagin prepared for the possibility of more havoc only days after an historic, life-saving evacuation of more than 2 million people from Hurricane Gustav.
Muddy Bodies Unclaimed In Haiti
Hurricane Ike's torrential rains swelled rivers across Haiti and sent floodwaters gushing into homes in the dead of night in one eastern town, killing at least 58 people.
Flooding also collapsed a bridge that had been the last land route to the food-short northern city of Gonaives, where residents fled to rooftops as waters rose for the second time in a week. Three bodies were found in Gonaives on Sunday, all victims of previous storms.
In all, four storms in less than a month have killed at least 319 people in the Western Hemisphere's poorest country.
But the rain stopped and floodwaters began to recede Monday morning in Gonaives, and residents who had taken refuge in the mountains began walking back to their mud-filled homes.
"People are starting to move back because they have nowhere to go," said Eric Mouillefarine, an official with the U.N. Development Program. "They want to protect their homes from looters."
Most of Sunday's deaths came in the Cabaret region, north of Port-au-Prince. A swollen river unleashed mudslides and floods, crushing homes and sending people fleeing in the middle of the night.
In the Always Funeral Home, 21 muddy bodies were piled in a dank room, unclaimed. Two of them were pregnant, one still clutching a small girl to her chest. Morgue workers roughly separated the bodies to count them.
On Monday, local civil defense director Henri Louis Praviel said authorities were searching for 16 more people, mostly children reported missing by their parents.
Waters reached chest-high levels before receding Sunday morning, leaving people to shovel mud from their houses. Others sat outside, surrounded by salvaged pots and mattresses, staring glumly at their collapsed homes.
"We took refuge in one room and waited there all night and prayed," said Sister Marie Denise, who was trapped by waist-high waters in the house she shares with four nuns. They evacuated to the nearby school they run after the waters receded.
"We don't know if one of our girls is among the dead," she said of her students.
No foreign aid has reached the town, Praviel said. Still, with the waters swiftly retreating and all roads leading into Cabaret still open, the town may be in better shape than isolated Gonaives, Haiti's fourth-largest city.
Pummeled by rains for four days last week during Tropical Storm Hanna, the city was cut off again Sunday when flooding caused the collapse of the Mirebalais bridge in central Haiti.
The falling water levels and returning refugees were hopeful signs, and U.N. peacekeepers and aid groups said they would overcome logistical difficulties and blocked roads to help the stranded city.
But water was still likely to keep running down from deforested mountains into the coastal flood plain.
Desperation was increasingly evident among people who have had little to eat or drink for days, prompting peacekeepers to beef up security.
A line of 3,000 people snaked around a warehouse-turned-U.N. shelter, and several hundred pushed and shoved to break down the door, only to be quickly subdued by Bolivian troops in riot gear.
As peacekeepers delivered aid to areas their trucks could reach, scores of young men splashed alongside, begging for help. One called out with a bullhorn: "Hey, hey, my friend. Give me some water!"
Food and fuel prices both skyrocketed, with gasoline reaching 500 Haitian gourdes (US$13) a gallon. And while relief workers in Gonaives said they had enough emergency food supplies for the next couple of days, distributing it is becoming ever more complicated.
Workers spent four hours handing out water and high-protein biscuits. But people were growing tired of relief food and started to demand rice, which has gone up 60 percent in price since the storms.
"We would like to eat some real food," said shelter resident Esaie St. Juste. "Rice, beans, sardines. Haitian people like real food."
Above Haiti's coastal floodplain, in the Artibonite Valley, authorities opened an overflowing dam, despite fears it could inundate more homes and possibly damage Haiti's "rice bowl," a farming area whose revival is key to rescuing the starving country.
Officials did not have immediate word on the situation below the dam, but Agriculture Minister Joanas Gay used state-run Radio Nacionale to urge Artibonite residents to "evacuate as soon as you can."