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.
Both the Republican and Democrat congressional leaders say they will keep talking, and 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.
