The hurricane warning issued to parts of the Gulf Coast includes the threat of life-threatening storm surge flooding. Evacuation orders have been put in place for some low-lying areas.
Louisiana Governor John Bel Edwards has declared a state of emergency ahead of the hurricane.
He said more than 1,000 National Guard troops had been mobilised with a number sent to New Orleans to monitor the drainage pumps there. "Anyone in low-lying areas... we are urging them to prepare now," he said.
A mandatory curfew from 18:00 (23:00 GMT) is in place in New Orleans, where residents from areas outside the city's levee system have been evacuated.
"Nate is at our doorstep, or will be soon," the city's Mayor Mitch Landrieu said, adding that the winds could cause significant power outages.
"We have been through this many, many times, there is no need to panic," he added.
A tropical storm warning is currently in effect for New Orleans.
Nate went past Mexico's Yucatan Peninsula - home to the popular beach resorts of Cancun and Playa del Carmen - on Friday night as it headed north, the NHC said.
Nate caused heavy rains, landslides and floods which blocked roads, destroyed bridges and damaged houses as it tore through central America.
At least 13 people died in Nicaragua, eight in Costa Rica, three in Honduras and one in El Salvador.
The tail of the storm is still causing problems in the region, where thousands have been forced to sleep in shelters and some 400,000 people in Costa Rica were reported to be without running water.