Laura was upgraded to a Category 4 storm as it approached the coasts of Texas and Louisiana on Wednesday.
The NHC warned local residents to “rush” to complete preparations.
Half a million have been told to leave. Laura and another storm, Marco, earlier hit the Caribbean, killing 24.
Marco has already struck Louisiana, bringing strong winds and heavy rain on Monday.
Initially it was feared that both storms would hit Louisiana as hurricanes within 48 hours of each other – an unprecedented event – but Marco was downgraded to a tropical storm.
Laura, on the other hand, has strengthened rapidly from a Category 3, gaining 70% in power in just 24 hours, to a Category 4, maximum sustained winds of 140mph (220km/h).
“To think that there would be a wall of water over two stories high coming on shore is very difficult for most to conceive, but that is what is going to happen,” National Weather Service meteorologist Benjamin Schott told reporters, as people were urged to leave the area.
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Evacuations are complicated by the Covid-19 pandemic. Texas Governor Greg Abbott urged families who could afford it to take refuge in hotels and motels to be distanced from others.
What can we expect from Hurricane Laura?
Early on Wednesday the NHC said satellite images had shown that Laura had undergone a remarkable intensification to become a “formidable hurricane”.
In a series of tweets, it said Laura was expected to bring “life-threatening hazards” and an “unsurvivable storm surge” to parts of the coast of the Gulf of Mexico.