It was about 280 miles (450 kilometers) south-southwest of the port city of Manzanillo on Saturday afternoon with maximum sustained winds of 60 mph (95 kph). It was moving north at 11kmh.
It threatens to bring torrential rains and major flooding, the NHC added.
The official forecast from the National Hurricane Center calls for Willa to weaken some before landfall on Tuesday, but the storm is still expected to be a unsafe major hurricane.
San Blas to Mazatlan, including Las Islas Marias, are under hurricane warnings while tropical storm warnings were issued for Playa Perula to San Blas and north of Mazatlan to Bahia Tempehuaya.
Models suggest, however that the storm has the potential to be formidable, as it will develop as the remnants of Category 5 Hurricane Willa, now in the eastern Pacific Ocean near Mexico's west coast, are drawn northeast into the Gulf of Mexico by the middle of the week.
The US National Hurricane centre said in an evening bulletin that the storm was "forecast to produce life-threatening storm surge, wind and rainfall over portions of southwestern and west-central Mexico beginning on [Wednesday]".
Hurricane-force winds extended 45 kmfrom the storm's center, and tropical storm-force winds were up to 1650 km out.
Willa is expected to douse coastal states Jalisco, Nayarit and Sinaloa with 15-30cm of rain, likely triggering flash floods and landslides, the NHC said.
By early this morning Willa's core was about 310 kilometres southeast of Acapulco with top sustained winds of 75 kph.
The hurricane was expected to pass over or near the Islas Marias - a set of islands about 60 miles (96 kilometres) offshore that include a nature preserve and a federal prison - early Tuesday. The additional rainfall could cause additional flooding in already saturated areas.
It's also the 21st named tropical storm or hurricane in the eastern Pacific so far in 2018.