Senators were still negotiating on the Senate floor as the clock turned midnight, but Trump's office issued a statement blaming opposition Democrats for the crisis.
Spokeswoman Sarah Sanders said the Democrats' insistence that the interim measure include protection for undocumented immigrants who arrived as children killed the deal.
"Senate Democrats own the Schumer Shutdown," she declared, referring to the minority leader, New York Senator Chuck Schumer, who met with Trump earlier Friday.
"Tonight, they put politics above our national security, military families, vulnerable children, and our country's ability to serve all Americans.
"We will not negotiate the status of unlawful immigrants while Democrats hold our lawful citizens hostage over their reckless demands," she warned.
Essential services and military operations will continue, but many American civil servants and diplomats could arrive at work on Monday only to find themselves sent home without pay until the political crisis is resolved.
Trump, who cancelled a trip weekend trip to his Florida golf resort to join 11th hour horsetrading accused the Democratic opposition of putting US troops and border security at risk to score political points.
But Democratic leaders accused Republicans of poisoning chances of a deal and pandering to Trump's populist base by refusing to fund a program that protects 700,000 "Dreamers" -- undocumented immigrants who arrived in the US as children -- from deportation.