After White House negotiations with the Democrats faltered yet again on Saturday, even a temporary measure to keep the federal government running appeared unlikely until the Senate returns for a full session on 26 December.
The first day of the shutdown saw thousands of government offices closed across the nation.
The Statue of Liberty was still open for tours, thanks to money from New York state, but many other landmark buildings – such as the White House visitor centre and the National Archives in Washington DC – were closed.
The US Post Office was still delivering mail as an independent agency.
While 420,000 workers were deemed essential and were expected to work unpaid, an additional 380,000 were to given a leave of absence, meaning they will stay home without pay.
The Senate had already passed legislation ensuring that workers will receive back pay, and the House was likely to follow suit.
No one in Washington knows how long the closures will last. Unlike other shutdowns, this one has lacked a sense of urgency, coming during the long weekend after Mr Trump had already declared Monday, Christmas Eve, a federal holiday.
Rather than work around the clock to try to end the shutdown, as they had done in the past, the leaders of the House and the Senate effectively closed up shop. But they did not rule out action if a deal were struck.
“Listen, anything can happen,” said Senate Majority Leader Mitch McConnell after he closed the Senate’s rare Saturday session hours after it opened.
But after ushering Vice President Mike Pence through the Capitol for another round of negotiations, the Republican chairman of the Appropriations Committee, Senator Richard Shelby of Alabama, said a quick end to the shutdown was “not probable”.
At the White House, Mr Trump hosted a lunch on Saturday with conservative politicians, including House Freedom Caucus chiefs Mark Meadows of North Carolina and Jim Jordan of Ohio, and several senators. Absent from the guest list were Republican leaders or any Democrats, who would be needed for a deal.
The president is insisting on $5bn (£3.95bn) for a border wall with Mexico. “I am in the White House, working hard,” tweeted the president, who cancelled his Florida holiday at Mar-a-Lago due to the shutdown.
Mr Trump’s re-election campaign sent out a fundraising email late on Saturday launching what he called “the most important membership program ever – the OFFICIAL BUILD THE WALL MEMBERSHIP”.
Mr Trump has savoured the prospect of a shutdown over the wall for months. Last week he said he would be “proud” to close down the government.
In recent days, though, Mr Trump tried to shift blame to Democrats for not acceding to his demand. He has given mixed messages on whether he would sign any bill into law.
Senators approved a bipartisan deal earlier in the week to keep the government open into February and provide $1.3bn (£1 bn) for border security projects, but not the wall.
Additional reporting by Associated Press
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies