(CNN) — Hurricane Gustav began to lash the southern Louisiana coastline early Monday as it moved closer to an expected midday landfall, according to the National Hurricane Center in Miami.

While forecasters said it could intensify a bit before moving inland, it will not likely be the Category 4 storm that had been predicted — a possibility that added urgency to mass evacuation orders in recent days.

Nearly all of the roughly 2 million people in coastal Louisiana and the New Orleans area had cleared out ahead of Hurricane Gustav on Sunday night.

Road, rail and air links out of New Orleans began to close as the first storm bands began to strike the city. But more than 1.9 million people had fled New Orleans and its surrounding parishes by Sunday night, and fewer than 10,000 people were thought to remain in New Orleans, Louisiana Gov. Bobby Jindal said, citing the city’s police chief.

New Orleans Mayor Ray Nagin had demanded an evacuation of the city, which still is recovering from 2005’s Hurricane Katrina. Forecasters warned Gustav — a Category 3 storm Sunday night — could hit Louisiana with devastating effect by early Monday afternoon.

Jindal said New Orleans’ levees should “barely hold or barely be overtopped” if the storm, as predicted Sunday evening, hit southwest of the city.

But even a slight shift to the east could bring “very significant flooding in these areas,” he said.

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written by Andrew