Texas emergency crews, slammed by tornadoes that killed at least 11 people overnight in the Dallas area and east Texas, were being stretched as a "very dangerous" blizzard was bearing down on other parts of the state Sunday.

Agencies raced to assess damage from the tornadoes, which leveled homes and downed power lines across much of Dallas County.

Related: Texas Storms, Tornadoes Leave at Least 11 Dead Around Dallas Area

Eight people were killed in Garland, which was hit by what Ari Sarsalari, a meteorologist for The Weather Channel, called "a violent tornado with a long path."

"It was terrifying," Randy Gore, who drove up to an impact scene where five people were killed, told NBC Dallas-Fort Worth. "It was heartbreaking, especially being the day after Christmas."

Officials in Collin County confirmed three deaths, two of them at a Copeville gas station that was destroyed in the storms.

Heavy rain of up to 6 inches was expected to hamper emergency crews late into the night in Dallas and surrounding areas, which were under a flash flood watch because the ground is already saturated, the National Weather Service said.

Missouri and southern Illinois were also getting a deluge, causing rivers and creeks to swell violently. At least 12 people were killed and another is missing after vehicles were swept off roads by floodwaters in separate incidents in both states, according to officials. In Missouri, Gov. Jay Nixon declared a state of emergency, saying that additional flooding and heavy rain were expected in the central and southern sections of the state, while the northern region was anticipating snow and freezing rain.

The storms also put the clamps on air travel. Almost 1,050 departures and arrivals had been canceled at Texas airports by 6 p.m. ET — 640 of them at Dallas-Fort Worth International alone. Almost 1,500 more were delayed.

Parts of several highways in northwest Texas were closed because of blowing snow and poor visibility, according to the Texas Department of Transportation. Amarillo got only about 3 inches of snow overnight but high winds have caused 3- to 4-foot drifts, according to the National Weather Service.

I have now been at the Austin airport for 16 hours and 25 minutes. — Everett Spence (@everett_spence) December 27, 2015

And "the crazy thing is it's going to get a lot worse than that," Sarsalari said.

Texas Gov. Greg Abbott warned residents in the western portion of the state to be careful on the roads in the midst of snow, ice and flood and cautioned the central and eastern parts of the state to remain vigilant in the face of tornado threats Sunday.

A strong cold front was moving into the state, with heavy winds gusting over 50 mph in areas. The combination of rain-filled clouds and plummeting temperatures meant a "life-threatening and crippling blizzard" was headed toward the Texas and Oklahoma panhandles, the weather service said.

Blizzard warnings were in effect until Monday afternoon across western and northern parts of the state, where whiteout conditions were expected from heavy snow blown by winds gusting to 65 mph, forecasters said.

"It's going to be a straight-up blizzard for eastern New Mexico [and the] Texas and Oklahoma panhandles, and then south of there and east of there, you've got some ice to deal with, and that's going to be very dangerous, as well," Sarsalari said.

Snow accumulations of 5 to 13 inches — with drifts to 10 feet — were likely in some areas of north Texas, southeast New Mexico and the Oklahoma panhandle.

Snow accumulations of 5 inches to upward of a foot — with drifts to 10 feet — were likely in some areas of north Texas, southeast New Mexico and the Oklahoma panhandle.

"We're still very concerned about eastern New Mexico, western Texas, streaming up into the Panhandle," said Danielle Banks, a meteorologist for The Weather Channel. "That cold air continues to filter in."

New Mexico Gov. Susana Martinez declared a state of emergency Sunday, saying 16 inches of snow had already fallen in some parts of the state, making roads impassable. "This is a dire situation, especially in the eastern half of the state where the storm has hit hardest and continues to dump snow, Martinez said.

An ice storm warning was posted for parts of western Oklahoma, where "numerous power outages will be likely," according to the National Weather Service.

The strong winds could drop wind chills to as low as 10 degrees below zero, it said.

Snow falling in downtown El Paso. pic.twitter.com/GmF896dGCI — Miguel Mendez (@NC9chiefphotog) December 27, 2015

More than two-dozen flooded roads remained closed in the eastern part of Oklahoma on Sunday afternoon, while Department of Transportation crews were treating highways and bridges with salt and sand across in the western section of the state, including Interstate 40 and the Oklahoma City metropolitan area.

Later in the week, as the system moves northeast, it will also likely spread snow and ice through the Midwest and into New England. Snow will develop Monday night across much of New England and parts of northern and eastern New York, forecasters said.

Boston could see some accumulation Monday night — and while the snow should remain northwest of New York City, Sunday's expected record high temperatures in the 60s will turn into a wintry mix of sleet and freezing rain within about 24 hours.