By Monday afternoon as much as 19in (48cm) of snow had already fallen in parts of New Jersey and Pennsylvania, and 17in (43cm) in New York City.
New York City and New Jersey have both declared a state of emergency.
The US National Weather Service said the storm will move up to New England, before tapering off on Tuesday.
Wind gusts of up to 50mph (80km/h) are also forecast for several days creating a blinding, blowing snow storm.
The storm has wrought havoc on local travel. New York City Mayor Bill de Blasio issued an order restricting non-essential travel from 06:00 local time (11:00 GMT) on Monday, and closing public schools on Tuesday.
New York state Governor Andrew Cuomo declared a state of emergency in New York City as well as 44 other counties.
"This is a dangerous situation," he said in a press conference on Monday. "A life-threatening-situation. Expect closures. It's going to get very bad very quickly."
In New Jersey, Governor Philip Murphy suspended the state's bus and rail operations on Monday. His emergency order allows authorities to shut roads and evacuate homes.
Major airports in the storm's path, including Newark Liberty International Airport, John F Kennedy Airport, and Philadelphia International Airport, have cancelled hundreds of fights. At New York's La Guardia Airport, all flights were suspended as of Monday morning.