Washington DC - The government shutdown entered its 35th day on Tuesday, matching a record set during Donald Trump's first presidency, as his administration warned of potential chaos at airports going into one of the busiest travel periods of the year.

The federal closure appears almost certain to become the longest in history, with no major breakthroughs expected before it goes into its sixth week at midnight – although there were fragile signs in Congress that an off-ramp was closer than ever.

The government has been grinding to a halt since Congress failed to approve funding past September 30, and pain has been mounting as welfare programs – including aid that helps millions of Americans afford groceries – hang in limbo.

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About 1.4 million federal workers, from air traffic controllers to park wardens, have been placed on enforced leave without pay or made to work for nothing.

The Trump administration sounded the alarm Tuesday over turmoil at airports nationwide if the shutdown drags into a sixth week, worsening staff shortages, snarling airport lines, and closing down sections of airspace.

Thanksgiving air travel is expected to set a new record this year, the AAA projected – with 5.8 million people set to fly domestically over the November 27 holiday.

More than 60,000 air traffic controllers and Transportation Security Administration officers are working without pay, and the White House has warned that increasing absenteeism could mean chaos at check-in lines.

Airport workers calling in sick rather than working without pay – leading to significant delays – was a major factor in Trump bringing an end to the 2019 shutdown, the joint-longest alongside the current stoppage.

Some lawmakers are hoping a slew of elections taking place in New York, Virginia, New Jersey, and California on Tuesday will provide the momentum they need to reopen the government.

But both sides remain dug in over the main sticking point – health care spending.

Democrats say they will only provide votes to end the funding lapse after a deal has been struck to extend expiring insurance subsidies that make vital health care affordable for millions of Americans.

But Republicans insist they will only address health care once Democrats have voted to switch the lights back on in Washington.

While both sides' leadership have shown little appetite for compromise, there have been signs of life on the back benches, with a handful of moderate Democrats working to find an escape hatch.

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A separate bipartisan group of four centrist House members unveiled a compromise framework Monday for lowering health insurance costs.

Democrats believe that millions of Americans seeing skyrocketing premiums as they enroll onto health insurance programs for next year will pressure Republicans into seeking compromise.

But Trump has held firm on refusing to negotiate, telling CBS News in an interview broadcast Sunday that he would "not be extorted."

The president has sought to apply his own pressure to force Democrats to cave, by threatening mass layoffs of federal workers and using the shutdown to target progressive priorities.

Last week, his administration threatened to cut off a vital aid program that helps 42 million Americans pay for groceries for the first time in its more than 60-year history, before the move was blocked by two courts.

Trump nevertheless insisted Tuesday – in apparent defiance of the court orders – that the food aid would be disbursed only after the government shutdown ends.

The White House later clarified, however, that it was "fully complying" with its legal obligations and was working to get partial SNAP payments "out the door as much as we can and as quickly as we can."