The US economy will take a billion-dollar hit if the government shutdown continues until the weekend, experts have predicted as Donald Trump showed no sign of backing down.

Some 25 per cent of the federal government is without funding after the US Congress and the president failed to approve a new spending package.

Standard & Poor's, the credit rating firm, estimated the shutdown would shave US$1.2 billion ($1.7b) off America's gross domestic product [GDP] every week.

Explained: Everything you need to know about a US government shutdown

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The shutdown began at midnight on Friday and shows little sign of ending as the one-week mark approaches. The departments of Homeland Security, Justice and Transportation are among those impacted.

Some 800,000 government workers are affected. While some of them continue to work, many will not get paid until the shutdown ends, impacting cash flows for scores of Americans.

Some have taken to social media to post about how it is affecting them with the hashtag "#shutdownstories", including voicing concerns over substantial bills that soon need paying.

At the heart of the shutdown, which sees affected government agencies and departments close their doors, is Donald Trump's insistence on new funding for his US-Mexico border wall.

Trump has said that he will not approve any new spending bill, which first needs to be agreed by the US Congress, unless it includes US$5b of border wall spending.

With the Democrats fiercely against the move and soon to take over the House of Representatives, a deal looks tricky.

Trump doubled down on his demand on Christmas Day when asked when government would fully reopen.

"I can't tell you when the government's going to be open. I can tell you it's not going to be open until we have a wall or fence, whatever they'd like to call it," Trump said, referring to Democrats against the border wall.

"I'll call it whatever they want, but it's all the same thing," he told reporters after a holiday video conference call with representatives from all five branches of the military stationed in Alaska, Bahrain, Guam and Qatar.

Trump argued that drug flows and human trafficking can only be stopped by a wall.

"We can't do it without a wall," he said.

"The only way you're going to do it is to have a physical barrier, meaning a wall. And if you don't have that then we're just not opening [government]."

Democrats have questioned the wisdom of spending money on a border wall, preferring to agree to improve fencing, technology and other border control measures.

John Deal, a Nasa contractor in Virginia, was one of those affected.

He told The Guardian that his son's tuition fees were due in four weeks.

"I budget ahead of time for Christmas and have saved for my son's college tuition," Deal said.

"The shutdown burden for my family is more [of a] concern for my [family's] living expense in the near future."