Daytime temperatures were expected to climb Monday into the 40s in much of southern Connecticut, Rhode Island and Massachusetts, where rain may fall as well.
That would help melt snow, though it could make what's there heavier and increase the risk of roof collapses. There were reports Sunday of a barn, a sports facility, commercial buildings and other buildings suffering cave-ins, Malloy said.
Freezing rain will change to rain as temperatures warm in the Northeast on Monday. But overnight lows will dip below freezing, causing melted snow to refreeze on roads.
A weak system will move through the area on Wednesday and will drop dustings of snow across the area, but the system should clear out by Thursday morning.
The mix made for a messy Monday morning commute into cities such as Boston, though schools remained closed there and in many other locales as the snow clean-up effort continued.
Flights resumed Sunday at Boston's Logan Airport and Amtrak restored limited service.
"We're working as hard as we can," Rhode Island Gov. Lincoln Chaffee said of efforts in his state. "We're seeing efforts every hour."
Lots and lots of snow
The blizzard that began burying the Northeast on Friday was historic by many measures -- most of all, by the amount of snow that fell.
In Hamden, Connecticut, for instance, 40 inches of snow made it difficult for plows to get on the roads. CNN iReporter Mia Orsatti said streets there had transformed into "white, wide, soft blanket(s) of snow."
Lesser depths still led to major headaches, especially when combined with hurricane-force wind gusts, storm surges and snow drifts.
"There's a ton of snow, and there's nowhere to put it," said Lena Berc of Boston, where 24.9 inches fell. "So it's really frustrating to find nooks and crannies."
Many still without power
About 270,000 utility customers were in the dark late Sunday, down from 635,000 a day earlier.
The outages were the result of a combination of whipping winds and power lines sagging, and sometimes snapping, under the weight of wet snow and ice.
"There was a phenomenal amount of trees that went down," Cantwell said, noting that no Scituate residents had power Sunday morning and estimating it may be Thursday before all the lights are back on.
For all the headaches in New England, however, many people were enjoying the wintry conditions.
iReporter Filipe Pereira said students at Wentworth Institute of Technology in Boston, who were set to return to class Monday, had enjoyed the weekend storm, engaging in massive snowball fights and building snowmen everywhere. People were even skiing down one street, he said. Students earlier took a series of photographs tracking the storm over 26 hours.
The streets around the small school were still a mess, but they were no longer closed.
"People have been going all over the roads with no problem," Pereira said.