As tens of thousands of workers in the airline industry stare down job losses starting Oct. 1, union leaders — with some support from company bosses — are pushing Congress to extend a multibillion-dollar federal aid program as part of the next coronavirus relief package.

A coalition of 13 labor groups said this week that an extension of a $25 billion payroll support program through March would keep workers in an industry that has been pummeled off the unemployment lines and ensure they can quickly return to their jobs once more people are ready to fly.

Failing to act, the unions said, could lead to mass layoffs, “causing potentially catastrophic consequences to this industry and our broader economy.”

Airline leaders were vocal in their push for the payroll program and a further $25 billion in loans in the spring when air travel almost collapsed. Now, with their companies no longer fighting for survival, they say they support the idea of an extension but emphasize that it’s the unions taking the lead in the campaign.

This week, more than 200 members of the House — Democrats and a few Republicans — signed a letter backing the proposal, but the prospects for finalizing a deal remain unclear. Democrats passed a new relief bill in May, when it looked like demand for air travel might recover quickly, and did not include more help for airlines. A bill unveiled by Republican leaders in the Senate this week proposes more help for airports but not airlines.

While the economy as whole has suffered and the highest-profile debate over the next aid bill has been on extending a $600 boost in unemployment benefits, the transportation sector continues to feel the effects of the pandemic acutely and is looking for another infusion of financial help. Transit agencies are seeking some $32 billion in aid. The state transportation departments responsible for building roads and bridges say they need $50 billion.

Aviation has been among the industries hit hardest as the virus has spread. The March aid bill, known as the Cares Act, singled out airlines for relief but imposed conditions on companies accepting money. Among them was a promise to not lay off employees until Oct. 1. The date seemed far off and likely to fall amid a recovery in passenger demand, but now the provision has set up the potential for dramatic job losses.

The rapid recovery airlines hoped for has stalled in recent weeks as coronavirus cases have soared and states have begun imposing quarantines on some out-of-state visitors.

On average, the Transportation Security Administration says it is screening about 660,000 people a day, a figure that has barely budged since early in the month and is down from 2.6 million at the same point last year.

According to the International Air Transport Association, 7.5 million flights have been canceled worldwide between January and July. Carriers are expected to lose $419 billion in revenue in 2020. Some analysts are now saying travel may not return to pre-pandemic levels until 2023 or 2024.

“The second quarter of 2020 was historic for the airline industry for all the wrong reasons,” Scott Kirby, chief executive of United Airlines, said during a recent earnings call. “At the beginning of April, we saw the sharpest, deepest drop in demand in history, far worse than 9/11 or the Great Recession or any other stress test scenario that anyone had modeled.”

The result is that the once-far-off Oct. 1 date is approaching and airlines are still reeling. American and United have issued formal notices saying they’re prepared to lay off as many as 61,000 employees. On Thursday, United told its pilots that it was now anticipating furloughing as many as a third of them — 3,900 — up from a previous estimate of 2,250.

Even without mass involuntary furloughs, there are clear signs the industry will be smaller.

Ed Bastian, chief executive of Delta Air Lines, said 17,000 employees — roughly 20 percent of the carrier’s workforce — have opted to leave the company. American is trimming the ranks of its management and administrative ranks by 5,000 workers.

Experts say the job losses from the pandemic will far eclipse those lost in the months after the 9/11 attacks. According to a report by the Bureau of Labor Statistics, more than 125,000 workers lost their jobs in the first 18 weeks after the attacks. The biggest share — 42 percent, or more than 44,000 — worked in the scheduled air transportation industry.

Aviation analyst Henry H. Harteveldt said the effect of the pandemic has been unprecedented and “absolutely destroyed demand for air travel.”

“There have been declines, but a certain amount of travel always continued, even during the depths of the recession,” Harteveldt said. “What we’ve never seen is a sustained depression in demand.”

After 9/11, airlines received $15 billion in bailout funds, $5 billion in grants and $10 billion in loans. But unlike in the Cares Act, the money was not earmarked for employee salaries. Mindful of that, unions pushed in March to ensure the money would go directly to front-line workers.

For flight attendants, particularly those who lived through 9/11, the pandemic has brought levels of anxiety many never thought possible. Those who have taken unpaid leaves find themselves worried about paying their bills, while those who have continued to fly worry about getting infected with the novel coronavirus, union leaders say.

“It’s so uncertain,” said Lyn Montgomery, president of TWU Local 556, which represents more than 17,000 Southwest flight attendants.

The airline said recently that enough workers have taken voluntary unpaid leaves of absence or opted to leave the company altogether that it will not furlough workers come Oct. 1.

Montgomery said that while the airline is better placed than most, “this is really unknown territory and that’s why we’ve been pushing for a second round of the Cares Act.”

While unions have made their push, airline leaders have taken a low-key approach, in contrast to their stance in the spring. Back then, Airlines For America, a group representing the biggest airlines, came forward to call for a $50 billion package.

Doug Parker, chief executive of American, said last week that the initial aid was needed to keep airlines in business but that the situation today is different.

More aid is “not something the airlines need as a means of keeping us solvent anymore, because we’ve all solved that problem, but certainly something we support because we support our team,” he said in an appearance on CNBC.

To the unions, the second round of payroll support is less about the airlines and more about the thousands of employees at risk of losing their jobs without an extension.

In a letter sent this week to House and Senate leaders, a bipartisan group of more than 220 House members voiced support for extending the program through the end of March, saying it would “ensure the U.S. airline system remains viable as a national security asset and engine of economic recovery once the pandemic is finally behind us.”

“Without further relief from Congress, mass layoffs among airline industry workers are inevitable — and their magnitude will eclipse those of any furloughs the industry has ever seen,” they wrote.