BUFFALO (CNN) -- New York Gov. Andrew Cuomo told residents in the Buffalo area to be ready to evacuate if they think floodwater caused by melting snow could reach their residences.
"It's not enough that your home has never flooded before," Cuomo said Sunday morning at a news conference. "There's always a first time, and this may be the first time."
He said people living in places that might flood should have a bag packed and clean out valuables from their basements. He urged them not to wait until the last minute to leave.
"Please err on the side of caution," he said.
Cuomo said dealing with flooding is worse than the snow.
"It's not water," he said Sunday. "It's a toxic brew. It has sewage in it; it has runoff in it."
Warming temperatures forecast for Sunday will start to melt 7 feet of snow that fell last week. Rain will add to the menace.
State officials aren't taking any chances. They've beefed up stockpiles of emergency supplies including generators and pumps and prepared nearly 180,000 sandbags.
Swift-water rescue teams also are in place, along with helicopters, in case anyone gets caught in a deluge of runoff waters. The New York Fire Department sent about 40 members of its incident management team and about 500 National Guardsmen arrived the area.
Temperatures should reach the high 40s on Sunday and go as high as 60 on Monday, according to the National Weather Service. Freezing temperatures are not expected again until Tuesday night.
The snow is melting fast in Depew, New York, said CNN iReporter Dawn Buck. A few days ago, it reached the railing of her backyard gazebo, she said, but on Sunday the snow was down to the floor.
"At least 3 feet of snow has melted so far," she said Sunday afternoon.
There's also the threat of more structure collapses as all the rain saturates the snow on the tops of buildings, making the load even heavier.
Several dozen roofs have already collapsed from just the weight of the snow, according to Erie County officials.
Cuomo said structural engineers will examine schools and other government buildings that might be in danger of roof collapses. He said most state government offices will reopen Monday.
'City of Good Neighbors'
One Buffalo man has a memorable souvenir of the storm.
Anthony Marchioli was so bored he rented a small snow tractor to clear driveways on his street, CNN affiliate WKBW reported.
On the way back from the rental business, he saw his wife standing in the street outside their house.
She was pregnant and her water had unexpectedly broken, so Marchioli put her on the tractor and pushed through whiteout snow to Mercy Hospital, WKBW reported.
Eleven hours later, the couple's third daughter was born. Her name: Loxley Storm Marchioli.
Erica Bartoe, a CNN iReporter from Hamburg, New York, said that people had come to her town from other areas to help shovel snow and drop off donations.
"Buffalo is called the City of Good Neighbors for a reason," she said. "There were people everywhere helping out."
Flooding threat extends to Tuesday
The area is under a flood warning. The National Weather Service says flood-prone areas will be inundated but warns there will be more widespread flooding, too.
"(We) expect 5 to 6 feet of water in some areas in a short period of time," Erie County Executive Mark Poloncarz said Saturday. The risk of flooding extends into Tuesday.
Commissioner Daniel Neaverth Jr. of the county Civil Defense/Disaster Preparedness Division told affiliate WGRZ that officials are "hoping for best, but we're also preparing for the worst."
It's a notion the governor echoed.
"Hopefully, we need none of this, and hopefully this was just an elaborate exercise in logistics that we will have done and then we will deconstruct, and everything will go back and people will say, 'Boy, the governor really made us waste our time bringing everything out there just to bring it back,'" Cuomo said Saturday. "I hope that happens."
Cuomo also said individuals have a responsibility to help deal with the storm. He urged people to clean out storm drains in front of their houses "so the water has some place to go."
A year's worth of snow in a week
The 86 inches that fell in some areas in three days last week is a typical year's worth of snow for Buffalo, according to the National Weather Service.
The deadly storm claimed 13 lives -- many because of heart attacks while clearing snow.
The death toll also includes one senior citizen who died of natural causes after or while being evacuated Thursday from a nursing home in Cheektowaga, officials said.
The storm also forced the NFL to reschedule Sunday's football game between the Buffalo Bills and the New York Jets. Instead of being played in Buffalo, it's now scheduled for Monday in Detroit.
For the Bills, even getting out of the Buffalo area had its complications. Before meeting at the stadium Friday morning to get on a bus to the airport, some of the players had to be picked up by snowmobile because of driving bans in certain areas, team spokesman Scott Berchtold said.