According to the local hotel association in Cabo, many tourists rushed to get out of the vacation spot leaving hotels with a 25 percent occupancy rate.
As many as 7,000 tourists are still left in the resort town. Some believe that they can still ride out the storm.
"We are staying at the Las Cascadas. It is pretty solid. There are not a lot of loose things to blow around. Everything is cement and concrete," said U.S. tourist Jim Patterson.
Officials are trying to evacuate some 10,000 people from shacks made of plastic sheetings, wood and even blankets. Many residents are not leaving in fear that their few possessions will be stolen.
The Mexican government says it may force an evacuation if people refuse to leave.
Meantime, U.S. airlines are allowing travelers to delay flights to Cabo San Lucas without the usual financial penalties for flight changes over the next few days. And cruise ships have cancelled port calls.
By Tuesday afternoon, Jimena had weakened slightly, with winds of 125 mph, still a major hurricane with potential to do huge damage.