A key vote is set to be held in a last-ditch attempt to reopen the US government before hundreds of thousands of federal workers are forced to start the working week with no pay.
Senate Republican leader Mitch McConnell has set a vote for 1am local time (6am GMT) on Monday to fund the government until 8 February and end the shutdown in the short term, allowing more time for talks.
Both houses of Congress – the Senate and House of Representatives – are set to reconvene on Sunday.
Mr McConnell said: "I assure you we will have the vote at 1am on Monday, unless there is a desire to have it sooner."
So far the impact of the shutdown, which began at midnight on Friday, has been limited to closing sites such as the Statue of Liberty.
However, the impact will be far greater if the stalemate spills into the new working week.
Republicans and Democrats have become embroiled in a blame game for the failure to pass a stop-gap funding measure by the 20 January deadline which is exactly a year since Donald Trump took office.
The main stumbling block is immigration and Mr Trump's refusal to fund a programme that protects 700,000 immigrants who arrived in the US as children from deportation – so-called Dreamers.
Democrats are far more concerned with Illegal Immigrants than they are with our great Military or Safety at our dangerous Southern Border. They could have easily made a deal but decided to play Shutdown politics instead. #WeNeedMoreRepublicansIn18 in order to power through mess!
— Donald J. Trump (@realDonaldTrump) 20 January 2018
Democrats have accused the President of pandering to his populist base while Mr Trump has accused them of being "far more concerned with illegal immigrants than they are with our great military or safety at our dangerous southern Border".
White House spokeswoman Sarah Huckabee Sanders said: "The President will not negotiate on immigration reform until Democrats stop playing games and re-open the government."
Mr Trump tweeted: "Democrats are holding our Military hostage over their desire to have unchecked illegal immigration. Can’t let that happen!"
The situation reached crisis point when Republican leaders failed to get the 60 votes needed in the Senate to pass a budget by midnight on Friday.
The legislation would have provided a fiscal rescue package to keep funding the government until 16 February which means currently the government has run out of money.
In further embarrassment for Mr Trump on the anniversary of his inauguration, hundreds of thousands of people took to the streets of US cities to march against the president and his policies.
The effects of the shutdown are set to intensify and although federal services and military activity are continuing, even active duty troops will not be paid until an agreement is thrashed out.
There have been four government shutdowns since 1990 and in the last one in 2013, more than 800,000 government workers were put on temporary leave.
Noelle Joll, 50, who works for the government, said: "We're just in a holding pattern. We just have to wait and see. It's scary."
A deal looked possible on Friday afternoon, when Mr Trump seemed to be close to an agreement with Democratic Senate minority leader Chuck Schumer on protecting Dreamers but no compromise was reached.
Congress met for a rare Saturday session, where leaders of both sides were meant to hammer out their differences to prevent the shutdown from stretching into Monday.
Instead the session descended into acrimony and Mr Schumer said trying to negotiate with Trump "was like negotiating with Jell-O (gelatin)."
He added: "It's impossible to negotiate with a constantly moving target. President Trump is so mercurial it's been impossible to get him to agree to anything."
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Mr McConnell said Mr Schumer "took the extraordinary step" of preventing the legislation from passing and thus "plunging the country into this totally avoidable mess".
Republicans have a tenuous one-seat majority in the Senate, and on Friday needed to lure some Democrats to their side to get the 60 votes needed to bring the motion forward but were 10 short.