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(CNN) —  

Sundays are for staying in – especially this week, as a winter storm sweeps across parts of the US.

Over 20 million people are under winter weather alerts across the northern Plains, Midwest and Northeast.

Heavy snow and possible blizzard conditions will stretch from northern Nebraska to northern Minnesota Sunday, the National Weather Service said. Heavy snow up to a foot in some places has already fallen across the Northern Plains and Upper Midwest over the last 24 hours.

Minnesota is grappling with slippery roads – so slippery that school buses were sliding off roadways.

The winter storm will center over northern Wisconsin and the Upper Peninsula of Michigan by Monday.

“Severe travel disruptions are likely for these areas through Monday,” the weather service said.

Additional snowfalls of 4 to 6 inches are expected across the Midwest and Northeast Sunday into Monday. Isolated locations, especially near the Great Lakes, could see up to a foot of additional snow.

Winter watches have also been issued for parts of upstate New York, New Hampshire, Vermont and parts of Massachusetts, CNN meteorologist Derek Van Dam said. The sweater weather will last through Tuesday, Van Dam said, with more freezing rain, ice and sleet.

A significant ice storm is forecast for areas of the Northeast and interior New England tonight through Tuesday morning. Ice totals of up to three-quarters of an inch are forecast, but some isolated locations may see up to an inch. This is likely to cause havoc for travelers in addition to downed trees and power lines.

Showers in the Midwest

On the south side of the storm, rain is forecast for areas of the Ohio River Valley down to the Gulf of Mexico. About 2 to 4 inches of heavy rain is forecast for areas of the Ohio River Valley, and flood watches have been issued throughout the region.

A line of showers will move back into Chicago Sunday night, the weather service said, which could also produce gusty winds. In the Detroit area, there’s a chance of thunderstorms Sunday, with up to 2 inches of rainfall possible by Monday, the weather service said.

“The good news is, it’s not a winter storm,” Van Dam said.

Snow showers are possible in parts of Detroit on Tuesday, the weather service said. Some “light snow” is also possible in Chicago on Monday, it said.

Severe storms are also forecast for parts of the Southeast today, where damaging winds and isolated tornadoes are the main threats.

CNN’s Haley Brink contributed to this report.