- Excessive heat warnings are issued for 14 states
- Forecasters warn of another round of storms Sunday
- "This is not a one-day situation; it is a multiday challenge," Virginia Gov. Bob McDonnell says
(CNN) -- Forecasters issued another round of excessive heat warnings Sunday for large swaths of the Midwest and Southeast as the regions dug out from deadly storms that left millions without power.
At least 12 people were killed, from Ohio to New Jersey, as a result of downed trees and power lines, according to officials. The destruction prompted state of emergency declarations by governors of Maryland, Ohio, West Virginia and Virginia.
"This is not a one-day situation; it is a multiday challenge," said Virginia Gov. Bob McDonnell, who called it the largest power outage unrelated to a hurricane in the state's history.
The National Weather Service issued warnings in 14 states, from Illinois to Georgia, indicating dangerous conditions for those unable to find refuge in a cool locale -- an advisory complicated by widespread power outages.
Forecasters, meanwhile, warned of another round of storms Sunday in areas hit hard by thunderstorms that barreled through Friday and Saturday and downed power lines.
Temps soar across the U.S. 
America is having a heat wave 
Storms leave millions without power 
Triple digit highs scorch the U.S. Nearly 4 million people were without power across the affected states at one point Saturday, a number that dropped by early Sunday morning to around 3 million.
In Ohio, where 900,000 were still without power late Saturday night, the governor was asking for federal help to get ice, gas and generators.
"I'm very concerned with the problems created by the combination of power outages and severe heat," said Ohio Gov. John Kasich, who said it could take up to a week to get the power back up to everybody in the state.
Kasich also called out the National Guard to check on and help the state's most vulnerable, primarily the elderly and the ill.
In West Virginia, power outages forced the closure of a large number of gas stations after pumps were rendered inoperable.
Brian Duckworth waited in line for gas for nearly two hours in Vienna, along the West-Virginia-Ohio border.
"I wouldn't even be here because I have plenty of gas in my truck," Duckworth told CNN affiliate WTAP. "But I have to get gas for my generators and some backup gas."
The storm also affected Amtrak service, including shutting down service between Washington and Philadelphia on Saturday morning.
But those most inconvenienced were aboard a train that ended up grinding to a halt Friday night in Prince, West Virginia, after trees blocked tracks both in front of and behind it, Amtrak spokesman Steve Kulm said.
By late Saturday night, the 232 passengers -- who stayed aboard the Chicago-bound train, which had air conditioning and food -- had been taken off and put on buses so they could reach their final destinations, according to Kulm.
Neighboring Virginia was also hard hit, with six deaths. At one point, the state had about 1 million power outages -- more than any other state.
The storms raced east Friday and into Saturday from Indiana through Ohio and into West Virginia and the nation's capital, carrying winds gusting as strong as 80 miles per hour.
New Jersey Gov. Chris Christie said there was a particular need for fuel, generators and communications equipment following the storm that caused enormous damage.
Those killed included two cousins in New Jersey, ages 2 and 7, who'd huddled with their families in a tent in Parvin State Park when strong winds felled a pine tree, crushing them. Their relatives all survived relatively unscathed, said Larry Ragonese, a spokesman for New Jersey's Department of Environmental Protection.
In Washington, a couple was electrocuted after they went outside to check on downed power lines. The husband was killed while the wife -- who is in critical condition at a local hospital with burns -- is expected to survive, said police spokesman Araz Alali.
Emergency rooms in Prince George's County, Maryland, filled up over the weekend by people looking to escape the heat, said Fran Phillips, deputy secretary for the state's Department of Health and Mental Hygiene. She noted that libraries and community centers across the state would stay open late to act as cooling centers.
Even in places where power was not disrupted, people with no air-conditioning were advised to spend the day in a library, a cooling center or some other such place to avoid heat exhaustion.
In Atlanta, where temperatures hit a record-breaking 106 degrees on Saturday and were projected to hit 103 degrees on Sunday, cooling centers were ordered open across the city.
CNN's Moni Basu, Greg Botelho and Nick Valencia contributed to this report.
