Travelers wait at a Southwest Airlines baggage counter to retrieve their bags after canceled flights at Los Angeles International Airport, Monday, Dec. 26, 2022, in Los Angeles. (AP Photo/Eugene Garcia)

CNN) — Air travelers in the United States hoping for clear skies on Tuesday following a disastrous week of weather-related flight cancellations and delays will have to extend their patience a few more days — particularly if they’re flying with troubled Southwest Airlines.

More than 3,000 flights within, into or out of the United States have already been canceled for Tuesday as of 5 p.m. ET, according to flight tracking website FlightAware.

Of those canceled flights, just over 2,600 were those of Southwest. That was almost two-thirds of all Southwest flights for Tuesday and a stunning 85% of all canceled flights in the United States.

By contrast, competitors Alaska Airlines had only 9% of its flights canceled and United Airlines had only 2%.

Airports most affected by the Tuesday cancellations are Denver International, followed by Harry Reid International Airport in Las Vegas, Chicago Midway International, Baltimore/Washington International, Nashville International and Dallas Love Field.

There were almost 5,200 delays as of 5 p.m. ET Tuesday.

Tuesday’s cancellations follow a full day of post-Christmas travel chaos, with 3,989 flights canceled on Monday — 2,909 of those being Southwest flights.

And Southwest’s Christmas struggles come during a year of troubles for the airline industry. Over the summer, nearly a quarter of US flights were delayed and thousands were canceled.

Southwest: Expect more days of cancellations

Southwest warns that this week’s cancellations and delays are expected to continue for several more days, with representatives saying the Dallas-based airline is planning to dial back its flight schedule in order to get operations on track.

Southwest Airlines CEO Bob Jordan told The Wall Street Journal the company plans to operate just over a third of its schedule in upcoming days to give itself the ability for crews to get into the right positions.

According to WSJ.com, Jordan added that reduced schedule could be extended.

“We had a tough day today. In all likelihood we’ll have another tough day tomorrow as we work our way out of this,” Jordan said in an interview Monday evening with WSJ.com.

“This is the largest scale event that I’ve ever seen.”

Multiplying problems

Southwest was hit particularly hard because of a cascade of issues.

The storm slammed two of its biggest hubs — Chicago and Denver — at a time when Covid and other winter ailments were stretching staff rosters. Southwest’s aggressive schedule and underinvestment have also been blamed.

The winter storm that swept across the country was ill-timed for travelers who had started pushing Christmas week flying numbers back toward pre-pandemic levels.

On Christmas Day, 3,178 flights were canceled and 6,870 were 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.

What can stranded passengers do?

At the Southwest ticket counter at Hartsfield-Jackson Atlanta International Airport on Tuesday morning, long lines were already building up as travelers waited to try to rebook flights or make connections.

And at Chicago’s Midway International, huge buildups of unclaimed bags piled up as passengers struggled to reclaim their luggage. There were similar scenes at other airports including Harry Reid in Las Vegas and William P. Hobby Airport in Houston.

Passenger Trisha Jones told CNN at the airport in Atlanta that she and her partner had been traveling for five days, trying to get home to Wichita, Kansas, after disembarking from a cruise at Fort Lauderdale, Florida.

After her flight out was canceled, she stayed with relatives then rerouted to Atlanta to pick up a connecting flight.

“We were fortunate, because we were in Fort Lauderdale — my family lives in the Tampa bay area so we were able to rent a car to go see my family for Christmas,” Jones said. “We’ve seen a lot of families who are sleeping on the floor, and it just breaks my heart.”

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. 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.”

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.

Southwest spokesperson: ‘Take care of yourself…keep your receipts’

A spokesperson for Southwest Airlines said the recent winter storm is to blame for the cascade of thousands of flight cancellations Monday and advanced cancellations Tuesday.

“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 in a press 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.”

McVay said that the company’s first priority right now is safety. “We want to make sure that we operate these flights safely and that we have the flight crews that have legal and sufficient time to operate these flights,” he stated.

“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.”

An announcement made in the terminal prior to the news conference apologized to customers, and said the next available SWA seats are on Saturday, December 31 and later. The agent said Southwest would be providing buses to area hotels and assured that “we will have sufficient rooms for all customers who are affected by this disruption.”

US government ‘concerned’ by cancellations

The US Department of Transportation issued a statement on Monday’s massive flight cancellations by Southwest Airlines, saying the agency is “concerned.”

“USDOT is concerned by Southwest’s unacceptable rate of cancellations and delays and 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.

Speaking to CNN on Tuesday, the vice president of the Southwest Airlines Pilots Association, Capt. Mike Santoro, said the problems facing Southwest were the worst disruptions he’d experienced in 16 years at the airline.

He described last week’s storm as a catalyst that helped trigger major technical issues.

“What went wrong is that our IT infrastructure for scheduling software is vastly outdated,” he said. “It can’t handle the number of pilots, flight attendants that we have in the system, with our complex route network.

“We don’t have the normal hub the other major airlines do. We fly a point-to-point network which can put our crews in the wrong places, without airplanes.”

He added: “It is frustrating for the pilots, the flight attendants and especially our passengers. We are tired of apologizing for Southwest, the pilots in the airline, our hearts go out to all of the passengers, they really do.”

Santoro, who said his association had been pressing the airline for some time to solve its structural problems, complained that pilots had also been affected by the current disruption.

“We have, over 10,000 pilots, not all flying at the same time, but imagine everyone is in the wrong city, without hotel assignments, and trying to find hotels?”

In other developments

• In hard-hit western New York, Buffalo International Airport said in its most recent tweet that it does not plan to resume passenger flights before 11 a.m. ET Wednesday, pushing back the expected reopening by another 24 hours later than previously anticipated.

• Greyhound, the largest provider of intercity bus service, issued a service alert on Tuesday morning stating many of its scheduled services in the upper northeast continued to be disrupted until further notice due to winter weather. Affected cities include Buffalo, Cleveland and Syracuse.