Now weakened slightly, packing 155 mph winds, Willa is moving north toward the southwest Mexican coast.
The storm is expected to make landfall Tuesday evening as a Category 3.
The major resort area of Puerto Vallarta is under a tropical storm warning -- as it is expected to face gusty winds, heavy rain and some flooding -- but not under a hurricane warning, because the worst part of the storm is forecast to miss the popular vacation spot.
Willa is expected to hit an underpopulated region of Southwest Mexico, staying well north of Puerto Vallarta.
Dangerous storm surge may threaten the coasts of the Isla Marias and west-central and southwestern Mexico on Tuesday.
The heavy rain may bring flash flooding and landslides to much of southwestern and west-central Mexico.
Some regions could see up to 18 inches of rain.
Willa is then expected to weaken after passing over the Sierra Madre mountains, and the remnants of the storm will likely bring significant rainfall to Texas.
Some portions of southern and central Texas could see as much as 4 inches of rain this week.
Heavy rain also is possible in Louisiana and Mississippi.