The Dallas-based airline has canceled more than half of its flights -- more than 2,300 total flights -- as 2:30 p.m. ET Monday.
LOS ANGELES -- Last week's winter weather travel mess is lingering like a vicious hangover into this week - and the headaches have been migraine-proportioned for Southwest Airlines, its CEO Bob Jordan, airline employees and most of all its frustrated passengers on Monday.
More than 3,900 flights within, into or out of the US had already been canceled by 10:50 p.m. ET Monday, according to flight tracking website FlightAware, while almost 8,200 flights had been delayed.
But Southwest accounts for a whopping share of those. None of the other U.S. carriers have canceled nearly as many flights or as much of their schedule as Southwest.
The Dallas-based airline had canceled 71% of its flights -- just over 2,900 total -- as of 10:10 p.m. ET Monday, according to FlightAware. At one point, the airline canceled around 300 flights in the span of a half hour Monday afternoon.
And it looks like the Southwest pain will spread into Tuesday.
More than 2,400 of those flights scheduled for Tuesday were already canceled as of 10:10 p.m. ET Monday. That's the lion's share of the just-over 2,600 flight cancellations reported so far for Tuesday for all US airlines.
At Los Angeles International Airport, about 106 Southwest flights had been canceled as of Monday evening, according to FlightAware, and another 27 were delayed. By comparison, 62 flights were canceled from all other airlines at LAX combined.
At Hollywood Burbank Airport, virtually every Southwest flight listed had been canceled.
On Christmas night, ahead of Monday's meltdown, Jordan told employees the airline has "a lot of issues in the operation right now."
CNN was provided a transcript of the message to Southwest employees by an aviation source.
Jordan told employees, "Part of what we're suffering is a lack of tools. We've talked an awful lot about modernizing the operation, and the need to do that."
On social media, customers are complaining loudly about long lines to speak with representatives, problems with lost bags and excessive wait times or busy signals on the airline's customer service telephone lines. One passenger told CNN her family was on the phone for 10 hours with Southwest.
A spokesperson for Southwest blamed the recent winter storm for the cancellations.
"As the storm continued to sweep across the country, it continued to impact many of our larger stations and so the cancellations just compiled one after another to 100 to 150 to 1,000," Jay McVay said at a news conference at Houston's William P. Hobby Airport on Monday night.
"With those cancellations and as a result, we end up with flight crews and airplanes that are out of place and not in the cities that they need to be in to continue to run our operations."
"We will do everything that we need to do to right the challenges that we've had right now," he said, including "hotels, ride assistance, vans ... rental cars to try and make sure these folks get home as quickly as possible."
He promised that all customers, even those who had already left the airport or made alternate arrangements on their own, would also be taken care of.
"If you've already left, take care of yourself, do what you need to do for your family, keep your receipts," McVay relayed. "We will make sure they are taken care of, that is not a question."
Southwest earlier responded in an emailed statement Monday afternoon emphasizing safety:
"With consecutive days of extreme winter weather across our network behind us, continuing challenges are impacting our Customers and Employees in a significant way that is unacceptable," the statement read.
"We're working with Safety at the forefront to urgently address wide-scale disruption. ... On the other side of this, we'll work to make things right for those we've let down, including our Employees."
Some of the airports seeing the biggest issues have been Denver, Chicago Midway, Baltimore/Washington, Dallas Love Field, Nashville and Las Vegas.
Calls made Monday afternoon by CNN to Southwest's customer service did not go through, so customers couldn't even get in the queue to speak to a representative. However, Southwest told CNN it is "fully staffed to answer calls."
The airline also says, "those whose flights have been canceled may request a full refund or receive a flight credit, which does not expire."
A tweet from Southwest directing customers to self-service options had more than 1,000 replies -- many of them angry -- around 6 p.m. ET.
One of the replies in part read: "Stop blaming the WEATHER! Had to buy a first class ticket on another airline but it TOOK OFF ON TIME! You still have our luggage with medication inside! Can't get through on the phone!"
In the Sunday night message to employees, Jordan said, "We need to be able to produce solutions faster." He said the airline is "committed to and invested in" improving its systems.
The US Department of Transportation issued a statement on Monday's massive flight cancellations by Southwest, saying the agency is "concerned."
"USDOT is concerned by Southwest's unacceptable rate of cancellations and delays & reports of lack of prompt customer service. The Department will examine whether cancellations were controllable and if Southwest is complying with its customer service plan," the agency tweeted.
The agency also tweeted a link to the Southwest customer service plan.
The president of the union that represents Southwest's flight attendants told CNN's Pamela Brown in an on-air interview Monday that those systems have left its members stranded.
"The phone system the company uses is just not working. They're just not manned with enough manpower in order to give the scheduling changes to flight attendants, and that's created a ripple effect that is creating chaos throughout the nation," Lyn Montgomery, president of TWU Local 556, told CNN.
She said some flight attendants needed to sleep in airports as a result.
Montgomery expressed outrage on behalf of workers and customers late Monday afternoon in a news release.
"The way Southwest Airlines has treated its flight crews can only be termed 'despicable,'" said Montgomery. "... Believe me, we know about stepping up and putting in long work hours when we are called to do so; we are flight attendants.
"But at this point, the many years of failure by management, despite many unions' demands to modernize, has left flight attendants fatigued, stranded, hungry and cold -- on Christmas!"
"The company's failures are happening year-round, but are particularly egregious on Christmas," Montgomery said. "Our customers struggled with it just as our thousands of flight attendants did."
Kathleen Bangs, a FlightAware spokesperson, said in on-air interview that Southwest's schedule includes shorter flights with tighter turnaround times that are causing some of the problems. "Those turnaround times bog things down," Bangs said.
CNN has reached out to the airline for comment on Jordan's video message.
If you've been left in the lurch and your efforts to reach a customer service agent are going nowhere, the founder of Scott's Cheap Flights suggests trying an international number.
"The main hotline for US airlines will be clogged with other passengers getting rebooked. To get through to an agent quickly, call any one of the airline's dozens of international offices" Scott Keyes said.
"Agents can handle your reservation just like US-based ones can, but there's virtually no wait to get through."
Click here to get international numbers that Southwest has previously posted.
It could be next week before this is all completely sorted out.
"When there's more than 10,000 flight cancellations over the past week, it takes time for airlines to work through and reaccommodate the backlog of travelers," Keyes told CNN Travel in an email.
"While it will depend on the weather forecast (which looks promising for much of the country) and what number of travelers wind up canceling their holiday plans, I'd expect that by next week, things will have largely returned to normal," Keyes said.
And why are so many people having trouble rebooking?
"One complicating factor for people hoping to get reaccommodated is the fact that there are so few available seats this season," Keyes said.
"That's both because Christmas and New Year is one of the most popular times of year for travel, and because the number of flights on the schedule this year is still down 15-20%, making the challenge even steeper for those needing to get rebooked."
A winter storm that swept across the US was ill-timed for travelers who had started pushing Christmas week flying numbers back toward pre-pandemic levels.
On Christmas Day, there were 3,178 flights canceled and 6,870 flight delayed, according to FlightAware.
On Christmas Eve, there were a total of 3,487 flights canceled, according to FlightAware.
Friday was the worst day of this streak with 5,934 cancellations, while Thursday saw almost 2,700 cancellations.
This megablast of winter weather across the eastern two-thirds of the nation is forecast to slowly moderate this week.
Reporting from ABC News and KABC contributed to this story.
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