Announcing its first Covid-19 patient, West Virginia Governor Jim Justice said: "We knew this was coming."
New York City said it is considering a lockdown similar to one in the San Francisco Bay area.
There have so far been 108 deaths in the US from coronavirus and more than 6,300 confirmed cases nationwide.
Globally, there are about 200,000 cases and nearly 8,000 people have died.
As the Trump administration seeks a $1tn economic stimulus package, US Treasury Secretary Steven Mnuchin reportedly warned Republican senators privately on Tuesday evening that if Congress fails to act, US unemployment could hit 20% - almost double the jobless rate during the Great Recession.