Paul had maximum sustained winds of 90 mph (145 mph) and was moving north at about 5 mph (8 kph), the U.S. National Hurricane Center in Miami, Florida said. Earlier Monday, it had maximum winds of 105 mph (170 kph) but it weakened slightly in the afternoon, downgrading to a Category 1 storm, the center said.
Forecasters predicted it could hit Mexico's Pacific coast by Wednesday.
A hurricane watch was issued for the tip of Baja California, which has been battered by two other hurricanes this season. The storm was on a course that would bring it just south of the peninsula late Tuesday before plowing into Mexico's Pacific coast near the resort of Mazatlan. At 2000 GMT, the storm was about 420 miles (675 kilometers) southwest of Cabo San Lucas.
"We ask ourselves why on this date in October?" said Francisco Cota, civil defense director for Los Cabos, adding that officials try to "stress that the season is not over yet."
Cota said officials planned to meet later to decide whether to evacuate people.
A light rain was beginning to fall in Cabo San Lucas as employees at the upscale Hotel Finisterra passed out sheets with the latest weather report to keep guests updated on the storm. They also were scrambling to organize indoor activities.
"We want to make sure we have entertainment for people during the storm to keep people tranquil and safe and provided with food and entertainment: movies, board games, interactive games with staff like Bingo," said Patricia Garcia, concierge at Hotel Finisterra.
Some, however, weren't sticking around for the storm. Long lines snaked from ticket counters at the airport in San Jose del Cabo.
Charles Bataglia, 38, from Chicago, cut his weeklong deep sea fishing trip short but was unable to get a flight back home. Instead he bought a ticket for Guadalajara in western Mexico.
"I didn't want to be trapped for four or five days. I have two young children. My wife works full time. I work full time," said Bataglia, standing at the airport in San Jose del Cabo. "There were definitely some difficulties trying to locate a ticket. Hopefully, I'll be able to find my way home through Guadalajara."
Stephanie Dalley, 50, a drug and alcohol counselor from Forestville, California, was glad she had already planned to leave Monday.
"We're just figuring it was good timing," she said.
Mexico was struck by two Pacific hurricanes last month. Hurricane John battered Baja California, killing five people and destroying 160 homes, while Hurricane Lane hit the resort town of Mazatlan, causing relatively minor damage.
Pablo Avila, 48, a construction worker who lives in a slum in San Jose del Cabo called Lomas de Guaymitas, said his flimsy shack always gets knocked down by storms and he was already planning on being evacuated for Paul.
"We are tired of this," he said. "Hurricane (John) affected everything, work, eating...it took all my clothes, everything."
Dennis Feltgen, a meteorologist at the U.S. National Weather Service, said a trough of low pressure has been sending storms this season on a track that takes them toward Mexico's Baja peninsula.
Both Atlantic and Pacific hurricane seasons, which end Nov. 30, have been normal this year, Feltgen said, adding that the U.S. has been fortunate to not be hit by any of the five hurricanes in 2006. The Atlantic had a record season last year with devastating storms, including Hurricane Katrina that slammed New Orleans, Louisiana.