Congress effectively gave up on breaking the impasse over US President Donald Trump's demands for border-wall funding, all but ensuring that the partial government shutdown will stretch at least into the start of the New Year, when Democrats retake control of the House.

Trump retreated from public view, hurling insults at Democrats over Twitter, as the House and the Senate convened for just minutes before gavelling closed until next week. During the brief session in the House, Republicans shot down a Democratic attempt to vote on legislation to reopen the government.

The halls of the Capitol were largely vacant, and leaders' offices were closed. There was no sign that negotiations were taking place. Instead, the two sides traded public recriminations.

Trump, in one of a series of Twitter attacks on Democrats, claimed that the dispute isn't even about the wall he long claimed Mexico would pay for. "This is only about the Dems not letting Donald Trump & the Republicans have a win," he wrote.

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Congressman Jim McGovern of Massachusetts, the Democrat who was denied on the House floor as he sought a vote to fund the government, said that it was urgent to end the shutdown, adding: "The only people who don't seem to be in any hurry are the Republican leadership and the President".

Benjamin Franklin ponders the shutdown. Photo / AP
Benjamin Franklin ponders the shutdown. Photo / AP

The country entered the sixth day of a government shutdown that has closed a quarter of the federal government and put off an estimated 350,000 workers, sending them home at risk of losing pay during the holiday season. Barring a surprise resolution, it will become the second-longest shutdown of the decade when the new, divided Congress convenes next week to open its 116th session.

"We have not been able to reach agreement, with regards to the leadership on both sides," Senator Pat Roberts, R, told reporters after presiding over a pro forma session in the Senate that lasted less than four minutes.

"In Dodge City, Kansas, they say a horse divided against itself cannot stand," Roberts added. "That's about where we are."

The Environmental Protection Agency and the Smithsonian museums, two departments that had followed the White House's direction to find money to stay open as long as possible, announced that reserve funds that had carried them through this week will end, closing the EPA today and the museum and the National Zoo starting next Thursday.

The Federal Emergency Management Agency said the National Flood Insurance Programme would not issue new policies during the shutdown, a potential nightmare for would-be home buyers who need the insurance before closing. Lawmakers from both parties have ripped the decision and called on the agency to reopen the programme.

According to a Reuters/Ipsos poll, 47 per cent of adults hold Trump responsible for the shutdown, while 33 per cent blame Democrats in Congress, and 7 per cent blame congressional Republicans.

Meanwhile, a day after Trump's surprise visit to American forces in Iraq and Germany, questions persisted about whether he had jeopardised the political neutrality of the US military by surfacing partisan attacks and signing red "Make America Great Again" hats for the troops.

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The President's behaviour - out of step with that of his predecessors - highlighted the struggle Pentagon leaders face in navigating an avowedly apolitical military through a hyperpartisan era in US politics, particularly under a commander in chief unafraid of breaking with established norms.

The Capitol is seen from the Russell Senate Office Building in Washington. Photo / AP
The Capitol is seen from the Russell Senate Office Building in Washington. Photo / AP

Trump defended his conduct. "CNN & others within the Fake News Universe were going wild about my signing MAGA hats for our military in Iraq and Germany," he wrote on Twitter. "If these brave young people ask me to sign their hat, I will sign. Can you imagine my saying NO? We brought or gave NO hats as the Fake News first reported!"

Critics also focused on the content of Trump's speeches during his trip. By making overtly political remarks to uniformed troops who were excited to meet their commander in chief, Trump risks undermining the trust Americans put in their armed forces.

Charles Blanchard, a former general counsel for the Army and the Air Force, said: "When it turns into a political rally, what do people see? They see enthusiastic soldiers clapping and yelling for a partisan message."

Robert Dallek, a presidential historian, said there's always an element of politics when presidents visit troops overseas but that Trump transgressed the line. "Once again, what you have with Trump is someone who bends the rules and violates the norms in order to make himself look special or exceptional."

The reason for the norms, according to Rosa Brooks, a law professor and national security expert at Georgetown University, is to ensure that an institution endowed by the American public with tremendous power "isn't being used for partisan ends. We have the line because we don't want to turn into a banana republic".

Grim days for unpaid workers

Three days, maybe four. That's how long Ethan James, 21, says he can realistically miss work before he's struggling.

So as the partial government shutdown stretched into its sixth day with no end in sight, James, a minimum-wage contractor sidelined from his job as an office worker at the Interior Department, was worried.

"I live cheque to cheque right now," he said, and risks missing his rent or phone payment.

Federal workers and contractors forced to stay home or work without pay are experiencing mounting stress. For those without a financial cushion, even a few days of lost wages could have dire consequences.

James said the contracting company he works for gave its employees a choice: take unpaid leave or dip into paid time-off entitlements. But James doesn't have any paid time off because he started the job just four months ago. His only option is forgoing pay.

"This is my full-time job, this is what I was putting my time into until I can save up to take a few classes," said James, who plans to study education and become a teacher. "I'm going to have to look for something else to sustain me."

Mary Morrow, a components engineer on contract for Nasa, is in the same predicament. In addition to caring for a family largely on her own, she's got a mortgage. "I have three teenage boys ... there are credit card bills and normal bills and it's nerve-wracking. It's scary."

- additional reporting: AP