"Bitterly cold weather will settle in behind this system from the Upper Midwest to New England," the National Weather Service says.
Areas around the Great Lakes, upstate New York and New England will also see a lot of snow. The storm has caused extensive power outages across Illinois and Indiana.
The storm dumped 19 inches of snow across the Chicago region on Sunday, making it the fifth-largest on record.
NPR's David Schaper in Chicago tells our Newscast unit that "many Chicagoans spent the morning trying to dig their cars out of waist deep snow drifts while other didn't even bother trying, knowing they'd likely get stuck a short time later on the still un-plowed sides streets."
David says Chicago public schools and most suburban and private schools are closed, but Chicago school buildings are open with some staff on hand for children with nowhere else to go.
The new storm approaching New England comes after last week's nor'easter dumped as much as 3 feet of snow on some regions.