The US government shutdown headed into its third day after frantic efforts by a bipartisan group of moderate senators failed to produce a compromise on immigration and spending.

"We have yet to reach an agreement on a path forward that would be acceptable for both sides," Senate Minority Leader Charles Schumer, (D), said, adding that talks would continue ahead of a procedural vote scheduled for this morning.

The effects of the shutdown over the weekend were relatively limited - halting rubbish pickup on National Park Service property, cancelling military reservists' drill plans, and switching off some government employees' cellphones.

But the shutdown continuing into today, the start of the work week in the US, means that hundreds of thousands of workers will stay home and key federal agencies will be affected. Passport and visa applications will go unprocessed, federal contractors will see payments delayed, and the Internal Revenue Service will slow its preparations for the coming tax season.

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The impasse continues as it was unclear whether the public would blame the Republicans, who control the White House and Congress, or Democrats taking a stand on immigration while closing government agencies.

The moderates' proposal - to link a three-week extension of government funding to the consideration of an immigration bill in the Senate - prompted Senate Majority Leader Mitch McConnell, (R), to announce that he would be willing to start debating immigration legislation if an agreement of the issue was not otherwise reached by early February.

"Let's step back from the brink," he said. "Let's stop victimising the American people and get back to work on their behalf."

But the pledge came with caveats that led senior Democratic aides to question whether it would ultimately be workable. Mindful of the failure of a sweeping immigration bill that passed the Senate in 2013 but languished in the House, Democrats want stronger assurances that the legislation they are demanding to protect young undocumented immigrants will ultimately become law.

Whether Republicans can find compromise on immigration remained as uncertain as ever, with no clear backing from House Republican leaders or President Trump, who showed no sign of retreating from his hard line on immigration.

A Fox News Quinnipiac University poll showed 73 per cent support for a bill protecting undocumented "Dreamers" and 21 per cent against.

Still, Senate Majority Whip John Cornyn, (R), said he was "optimistic" the Senate would vote to break the impasse. Schumer, he said, "wants to just give everybody a chance to chew on it and sort of understand it, and so that's why he didn't want to have the vote tonight".

Matt House, a spokesman for Schumer, said the Democrats "made some reasonable offers to Senator McConnell and he hasn't accepted them yet. The caucus is waiting for him to move some in our direction". The decision ultimately belonged to McConnell and Schumer.

"We're trying to be helpful in showing them that there is a path forward," said Senator Susan Collins, (R), who hosted more than a dozen fellow moderates in her office for a meeting. Among the participants were a number of Democrats who are seeking re-election in states Trump won in 2016.

Trump wrote that if the "stalemate continues," then Republicans should use the "Nuclear Option" to rewrite Senate rules and try to pass a long-term spending bill with a simple majority rather than the 60 votes needed to pass most legislation - a notion Trump has previously floated to McConnell's repeated dismissal.

The President otherwise remained quiet, heeding the advice of senior advisers who argued that he has the upper hand over Schumer and the Democrats and that they would soon be forced to capitulate.

On the Senate floor, Schumer showed no signs of caving. "Not only do they not consult us, but they can't even get on the same page with their own president. The congressional leaders tell me to negotiate with President Trump; President Trump tells me to figure it out with the congressional leaders. This political Catch-22, never seen before, has driven our government to dysfunction."

Local region could be hit the hardest

For the Washington region, which boasts the largest concentration of federal employees and contractors in the US, the shutdown could have particularly serious consequences.

"No one has more to lose from shutdown brinkmanship than the capital region," Senator Mark Warner, (D), said. "If you viewed this as a company town, it's like the factory shut down, and we don't know when it's going to reopen," Congressman Gerald Connolly, (D), said.

Up to a quarter of the region's workforce of 3.2 million people could be affected, according to Stephen Fuller, an economist at George Mason University. He noted that 367,000 federal employees and 450,000 contractors live in the area. He said 25 to 30 per cent of the region's economy is dependent on federal payroll and procurement spending. "It's hard to point to an economy in the country where one company represents between 25 and 30 per cent of local GDP.".

Connolly cited statistics showing the region could lose US$200 million per day in economic productivity.