A man clears snow from the sidewalk in front of his home, March 23, 2015. Scott Olson/Getty Images

After damaging tornadoes and significant flooding in the Deep South of the U.S., Americans in the southern Great Plains and Rocky Mountain states braced for a major winter storm Saturday. The region could see blizzard conditions with heavy snowfall, the National Weather Service predicted.

As many as 15 million people across the U.S. faced severe weather threats Saturday, some of them travelers hoping to head home following a holiday weekend away, CNN reported. A cold front is expected to head into West Texas, bringing a mix of snow, sleet and freezing rain.

"By Sunday morning, the snow, sleet and freezing rain will expand northeast across the southern Plains," the National Weather Service said. "Heavy snowfall amounts of 10 to 18 inches are forecast through Sunday evening across much of western/northwestern Texas, with 18 [to] 24 inches forecast across portions of New Mexico."

Major cities such as the Texas capital of Austin, Dallas, Houston and New Orleans could see severe weather. The precipitation combined with high winds already has some 1.2 million people under a blizzard warning from New Mexico to the Oklahoma and Texas panhandles, according to CNN.

"The blizzard conditions could bring travel to a halt along parts of highways [Interstate]-25 and I-40 in the region," AccuWeather Senior Meteorologist Alex Sosnowski said.

The potentially heavy snowfall would come on the heels of torrential rains in the southern U.S. that caused considerable flooding. After a tornado touched down in Birmingham Friday, Alabama was still on alert for flooding Saturday. The severe weather in recent days killed at least 17 people, destroyed homes and broke rainfall records across the South, NBC News reported. The storm system that began Wednesday produced some 25 tornadoes over three days. Unseasonably warm weather helped spawn the system responsible for the devastation in spots throughout Arkansas, Mississippi and Tennessee.