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.