The transportation secretary, Sean Duffy, is warning that federal authorities may be forced to close airspace in parts of the country if the government shutdown stretches into next week. 

Speaking to reporters on Tuesday, Mr. Duffy said that air traffic controllers are about to miss another paycheck. He said that he has heard from air traffic controllers who said “many” can “navigate missing one paycheck,” but “none” of them can manage missing two paychecks.

“So if, if you bring us to a week from today, Democrats, you will see mass chaos,” he said. “You will see mass flight delays. You’ll see mass cancellations, and you may see us close certain parts of the airspace, because we just cannot manage it, because we don’t have the air traffic controllers.”

Mr. Duffy has warned about staffing shortages among air traffic controllers, who have been required to work without pay since the shutdown began. The transportation secretary said that the system is currently facing a shortage of between 2,000 and 3,000 air traffic controllers. 

The warning of “mass chaos” comes as Senate Democrats blocked a vote to reopen the government for the 14th time, meaning the shutdown is now the longest in American history.

There were potential signs that the lawmakers may be making progress toward ending the stalemate, as a bipartisan group of lawmakers in the House released a framework of a deal that would extend the Obamacare subsidies set to expire at the end of the year. Democrats have said they would not pass a funding bill without a deal to extend the subsidies. However, it is unclear if the bill would pass the Senate. 

As the shutdown has dragged on, air traffic controllers have been calling out of work and looking for other jobs to pay the bills. The FAA said on Friday that “nearly 80 percent of air traffic controllers are absent at New York–area facilities.”

On Sunday, the FAA said that 84 percent of flight delays were due to staffing shortages, up from 5 percent between January and September. By Tuesday afternoon, a flight tracking website, FlightAware.com, reported that there had been 1,932 delays within, to, or out of American airports and 51 cancellations.  

The staffing shortages have led some Americans to question whether it is safe to fly. Mr. Duffy told CNBC’s “Squawk Box” on Monday that there will be more cancellations of flights and delays “because we slow traffic down” as a “tool that we have to keep the system safe” due to the shortage of air traffic controllers. 

He added that if the government believed air travel was not safe, it would “shut the whole airspace down.”

“We won’t let people travel,” he said. “We’re not there at this point. It’s just significant delays.”

Some lawmakers have predicted that Congress will be able to reopen the government after Tuesday’s elections.