Jimena may bring some relief to northwestern Mexico's drought and dump rain on southern Arizona and New Mexico, said Richard Pasch, senior hurricane specialist at the National Hurricane Center in Miami.
The storm is less likely to douse southern California's wildfires, but "that's still a possibility and we're keeping our fingers crossed," he said.
Police, firefighters and navy personnel drove through shantytowns, trying to persuade some 10,000 people to evacuate shacks made of plastic sheeting, wood, reeds and even blankets.
"For the safety of you and your family, board a vehicle or head to the nearest shelter," firefighter Ricardo Villalobos bellowed over a loudspeaker as his fire truck wound its way through the sand streets of Colonia Obrera, a slum built along a stream bed that regularly springs to life when a hurricane hits.
Asked how many people were paying attention, he noted wryly, "Not many."
Many residents feared that their few possessions - a TV, radio or refrigerator - would be stolen if they left.
Jose Miguel Leyva, a cab driver, nailed another plastic sheet to his rickety wood framed shack, vowing to stick it out as long as he could.
"We're putting all we can into the house," Leyva said. "They told us to go to a shelter. If it gets bad maybe we will. We can go in my car."
Roberto Hernandez, a community organizer, said he and other activists had formed a security brigade to ride out the storm and watch over their neighbors' possessions. "A lot of times, people steal their furniture, or whatever they can find," Hernandez said.
But Miguel Angel Juarez, an unemployed iron worker, packed clothing and his countertop gas grill into the trunk of his car before taking his family to a shelter.
"I'm not staying here," he said, eyeing the stream bed that runs a few feet from his front door. "They say that when it rains here, this becomes a river."
The government warned that those who refuse to evacuate would be forced to do so.
Organizers of an international financial meeting scheduled for Cabo San Lucas this week decided to move their conference to Mexico City.
Many tourists rushed to leave, leaving hotels with a 25 percent occupancy rate, according to the local hotel association. The group estimated 7,000 tourists were left in Los Cabos.
But on Cabos' famous beaches, some tourists were doing just the opposite, jumping into the Pacific to play in the hurricane's big waves.
Early Tuesday, Jimena was a Category 4 storm with maximum sustained winds near 155 mph (250 kph) and was moving north-northwest near 12 mph (19 kph), the U.S. National Hurricane Center in Miami reported. It was centered about 155 miles (250 kilometers) south of Cabo San Lucas.
Hurricane force winds extending as far as 45 miles (75 kilometers) and tropical storm force winds 140 miles (220 kilometers).
Hurricanes reach Category 5 at 156 mph (250 kph).
Farther out in the Pacific, Tropical Depression Kevin had top winds of 35 mph (55 kph) and was expected to weaken to a remnant low later in the day or Monday night. It was centered 830 miles (1,335 kilometers) west-southwest of the Baja peninsula's southern tip.
Associated Press writers Martha Mendoza and Julie Watson in Mexico City contributed to this report.