Applications for jobless benefits remained high last week, even as the collapse of stimulus talks in Washington raised fears of a new wave of layoffs.

Unemployment filings have fallen swiftly from their peak of more than six million last spring. But that progress has recently stalled at a level far higher than the worst weeks of past recessions. That pattern continued last week, the Labor Department said Thursday: More than 800,000 Americans filed new applications for state benefits, before adjusting for seasonal variations, roughly in line with where the total has been since early August.

“The level of claims is still staggeringly high,” said Daniel Zhao, senior economist at the career site Glassdoor. “We’re seeing evidence that the recovery is slowing down, whether it’s in slowing payroll gains or in the sluggish improvement in jobless claims.”

That slowdown comes as trillions of dollars in government aid to households and businesses has dried up. Prospects for a new stimulus package, already dubious in a divided Washington, appeared to fall apart this week when President Trump said he was pulling out of negotiations. Economists across the ideological spectrum warn that the loss of federal help will lead to more layoffs and business failures, and more pain for families.

The continued high level of jobless claims, combined with large monthly job gains, highlights the remarkable level of churn still roiling the U.S. labor market. Companies are continuing to rehire workers as they reopen, even as other companies cut jobs in response to still-depressed demand for goods and services. The result is a job market that is being pulled in two directions at once — and economic data that can appear to tell contradictory stories.

Adding to the challenge for analysts and forecasters, the pandemic has thrown the data itself into disarray. For the second week in a row, the jobless claims data carried a Golden-State-size asterisk: California last month announced that it would temporarily stop accepting new unemployment applications while it addressed a huge processing backlog and installed procedures to weed out fraud.

In the absence of up-to-date data, the Labor Department is assuming California’s claim number was unchanged from its pre-shutdown figure of more than 225,000 applications, or more than a quarter of the national total. The state began accepting new filings this week, and is expected to resume reporting data in time for next week’s report.

While the lack of data from California makes week-to-week comparisons difficult, the bigger picture is clear: The economic recovery is losing momentum, even as millions of Americans remain out of work.

Monthly jobs data released last week showed that job growth slowed sharply in September, and that last spring’s temporary furloughs are increasingly turning into permanent job losses. Major corporations like Disney and Allstate have announced thousands of new job cuts. And with winter approaching, restaurants and other businesses that were able to shift operations outdoors during warmer weather could be forced to pull back anew.

Separate data from the Census Bureau on Wednesday showed that 8.3 million Americans reported being behind on rent in mid-September, and 3.8 million reported that they were likely to be evicted in the next two months. Both figures have changed little since August.

“It seems increasingly unlikely that we’ll have a deal before the election, and bills are due now,” Mr. Zhao said. “Every week that passes puts extra pressure on workers’ households and small businesses, so any delay in the stimulus is going to have a meaningful impact on Americans.”

The situation is particularly dire for people who lost their jobs early in the pandemic, many of whom are now nearing the end of their unemployment benefits.

Last week was the 29th week since mass layoffs began in March. In most states, regular unemployment benefits last just 26 weeks, meaning that many people have already exhausted their benefits.

In March, Congress created a program funded by the federal government for people whose state benefits have expired. The number of recipients under that program, Pandemic Emergency Unemployment Compensation, swelled to nearly two million in mid-September, up from 1.4 million a month earlier.

The program adds only 13 weeks of additional benefits, however, so people who lost their jobs in March will receive those benefits only until mid-December. And the entire program will expire at the end of the year if Congress doesn’t extend it.

A separate program, which existed before the pandemic, offers an additional 13 to 20 weeks of benefits, depending on the state. But the benefits are based on state economic conditions, and the rapid decline in the unemployment rate means that workers in several states, including Idaho, Wyoming and Utah, would no longer qualify for it. Missouri will join their ranks next week.

Another emergency program, Pandemic Unemployment Assistance, also expires at the end of the year. That program covers freelancers, self-employed workers, part-timers and others who don’t qualify for benefits under the regular unemployment system. More than 460,000 people filed new applications under the program last week, and millions are receiving benefits in total.

The net result is that potentially millions of workers could see their benefits expire this winter. Epidemiologists warn that cases of the coronavirus are likely to rise as temperatures drop, and winter weather could reduce job opportunities.

“People are going to have their backs against the wall, and it’s pretty much the worst time of the year for the program to end,” said AnnElizabeth Konkel, an economist at the employment site Indeed.