Recriminations have begun over the failure of the US Senate to pass a new budget and prevent the shutdown of many federal services.
A bill to fund the federal government for the coming weeks did not receive the required 60 votes by the deadline of midnight on Friday.
President Trump accused the Democrats of putting politics above the interests of the American people.
The Democrats blame him for rejecting bipartisan compromise proposals.
Negotiations in both houses of Congress continued on Saturday, Senate Republican leader Mitch McConnell said the chamber would be back in session on Sunday to try to end the impasse.
The White House budget chief has expressed optimism that a resolution will be found before Monday.
But if not, hundreds of thousands of federal workers face the prospect of no work and shuttered offices at the start of the working week.
The last government shutdown was in 2013, and lasted for 16 days.
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!
Why can the two sides not agree?
This is the first time a government shutdown has happened while one party, the Republicans, controls both Congress and the White House.
The vote on Friday was 50-49, falling far short of the 60 needed to advance the bill. With a 51-seat majority in the Senate, the Republicans did not have enough seats to pass the bill without some support from the Democrats.
They want funding for border security - including the border wall - and immigration reforms, as well as increased military spending.
The Democrats have demanded protection from deportation of more than 700,000 undocumented immigrants who entered the US as children.
This could be a protracted, ugly fight
Anthony Zurcher, BBC News, Washington
The game of chicken ended with a head-on crash.
Republicans are anxious to label this the "Schumer shutdown" and, essentially, they're right. Chuck Schumer and his fellow Democrats (with the help of a few Republicans) blocked a bill that would have kept the government open - at least temporarily.
Determining responsibility and apportioning blame, however, are two decidedly different endeavours.
Democrats will argue that they had a deal with the president on their bipartisan compromise that included immigration reform - only to have him back away during that fateful obscenity-laden Oval Office meeting last week. Republicans will frame this as liberals putting undocumented immigrant protections over military readiness and health insurance for poor kids.
The winner of the blame game has yet to be decided. Generally, the loser in these types of showdowns is the party entering the fight with the lowest popularity - bad news for Mr Trump and the Republicans.
The good news, for both sides, is that their political bases will be thrilled they are playing hardball. Midterm election years, like 2018, tend to encourage this kind of rally-the-base manoeuvres.
Now that the line has been crossed, this could become a protracted, ugly fight.
What is a government shutdown?
The US budget must be approved by 1 October - the start of the federal financial year.....read more
