MIAMI, Florida (CNN) -- Hurricane Gustav picked up strength as it moved over the northwestern Caribbean Sea Friday night, pursuing a projected path aimed at the Gulf Coast.
At least 51 people died in southwestern Haiti and eight were killed in neighboring Dominican Republic as Gustav, then a tropical storm, passed through Wednesday, officials said.
By Friday, Gustav reached hurricane strength with maximum sustained winds of 80 mph (129 kph) as it passed over the Caribbean.
Shortly before 11 p.m. ET, the storm was moving northwest at about 10 mph (17 kph) as it bore down on the Cayman Islands. Hours earlier, it had moved away from Jamaica, where it left downed trees and damaged houses in its wake.
Fear and uncertainty about Gustav's position and strength by Monday sent emergency officials and politicians in the United States scrambling to prepare for a possible landfall of a major hurricane somewhere along the Gulf Coast. Watch how New Orleans prepares for Gustav »
Officials in New Orleans, Louisiana, warned residents that they'll be on their own if they ignore orders from police with bullhorns directing them to evacuate, The Associated Press reported.
Jerry Sneed, the city's emergency preparedness director, said the Superdome would be locked and there would be no shelter of last resort if residents decided to accept "all responsibility for themselves and their loved ones," the AP reported.
Forecasters expected the storm to turn toward the northwest later Friday and continue on that track over the weekend. On that path, "The center of Gustav will pass near or over the Cayman Islands later today, over the western portions of Cuba on Saturday, and into the southern Gulf of Mexico on Sunday," the center said. See Gustav's projected path »
Gulf of Mexico conditions also appear conducive to a major hurricane, the forecasters said. iReport.com: Gustav washes away bridge
Beyond Jamaica, oil companies began to pull workers off drill rigs in the Gulf of Mexico, and Mississippi joined Louisiana in declaring a state of emergency as forecasters warned of a U.S. landfall next week.
State officials along the Gulf Coast have begun warning residents to prepare for the storm. About 3,000 Louisiana National Guard troops began reporting for duty Thursday, and the state put another 2,000 on alert, Louisiana Gov. Bobby Jindal said.
National Guard satellite communication teams will be assigned to emergency operations centers in coastal parishes to ensure those centers can remain in touch with state officials in Baton Rouge, Jindal said.
In New Orleans, which has yet to fully recover from Hurricane Katrina, Mayor C. Ray Nagin on Thursday urged citizens living in FEMA units to make evacuation plans in case city officials order them to leave. Watch New Orleans' mayor say his city is ready for Gustav »
Elsewhere in the "cone of certainty," Mississippi Gov. Haley Barbour said Hurricane Katrina victims living in government-issued trailers or mobile homes along his state's coast will begin evacuating this weekend.
Louisiana and Mississippi are still recovering from Hurricane Katrina, which killed more than 1,800 when it slammed ashore near the state line on August 29, 2005.
The hurricane center's five-day chart places a possible landfall anywhere from Corpus Christi, Texas, eastward to Panama City, Florida, with Gustav being a Category 3 storm by Tuesday evening. New Orleans, devastated by Hurricane Katrina three years ago Friday, is at the center of the projected path. Watch the homeland security secretary's warning to residents »
Forecasters, however, stressed their uncertainty in a discussion published late Thursday.
"Since track forecasts are always subject to large errors at three to five days, it is simply impossible at this time to determine exactly where and when Gustav will make final landfall," the hurricane center's forecasters said.
While Gustav will go nowhere near Minneapolis-St. Paul, Minnesota, where the Republican National Convention is set to begin Monday, the political implications of a Gulf Coast landfall could rain on Sen. John McCain's celebration.
Republican officials said their convention might be delayed by a major hurricane making landfall.
President Bush was criticized for attending political events -- including a brief stop to mark McCain's birthday -- after Hurricane Katrina left most of New Orleans flooded in 2005.
Bush is set to speak Monday at the GOP convention. White House spokeswoman Dana Perino told reporters that Bush is keeping an eye on developments but said it is premature to discuss any changes to his schedule.
Earlier Friday, the storm blasted Jamaica, killing four people as it downed trees and damaged homes, the National Emergency Operations Center in Jamaica said.
"It is total devastation everywhere," the councilor for the Manchioneal division, Alston Hunter, told the Jamaican Gleaner newspaper. "Several residents are now crammed into disaster shelters here in east Portland, and the weather continues to make the situation worse."
The Jamaican government downgraded its hurricane warning to a tropical storm warning, the center said.
A hurricane warning -- meaning that sustained winds of at least 74 mph (119 kph) are expected within a day -- remained in effect for the Cayman Islands, and the Cuban government issued a hurricane warning for the western portion of the island. A tropical storm warning was issued for central Cuba, the hurricane center said.
Even as it moved away from Jamaica, Gustav was still dumping rain that was likely to total 6 to 12 inches across Jamaica, the hurricane center said. That amount was also expected across the Cayman Islands and western Cuba, with maximum isolated amounts of 25 inches possible, the hurricane center said.
"These rains will likely produce life-threatening flash floods and mudslides," the center said. The forecasters said coastal storm surge flooding of 2 to 5 feet above normal tide level was possible in the Cayman Islands, and of 8 to 13 feet possible in western Cuba, near where the center of Gustav passes.
Meanwhile, Tropical Storm Hanna passed north of the Leeward Islands Friday with maximum sustained winds of 50 mph (80 kph), the hurricane center said.
"Gradual" strengthening is forecast, and Hanna could be near hurricane strength on Sunday, the center said.
Forecasters say the storm will likely pass well away from the Virgin Islands and Puerto Rico Friday night into Saturday. On Sunday, it will be northeast of the southeastern Bahamas, the center said, but the extended forecast calls for it to make a southerly turn toward the Bahamas.
CNN's Eric Marrapodi, Sean Callebs and Barbara Starr contributed to this report.