"If people are thinking about evacuating they need to do it now," sergeant Markus Smith from Louisiana state police, said.
However, the US army corps of engineers said it was "confident" that the network of levees, pumps and drainage canals would protect New Orleans from serious flooding.
Schools in the city and its suburbs were closed on Monday and motorists were urged to stay off the road.
New Orleans is still rebuilding from the devastation wrought by Hurricane Katrina which destroyed levees and flooded most of the low-lying city four years ago.
Ida was downgraded to a tropical storm on Monday as it passed Mexico's Yucatan Peninsula, dumping torrential rain but causing no casualties or major damage in the area.
Hurricane Ida, coupled with a low pressure system in the Pacific, caused heavy flooding in the Central American country of El Salvador that killed 136 people and left 13,680 people homeless.
Mauricio Funes, the country's president, declared a state of emergency, saying the damage sustained was "incalculable".