As the clock struck midnight in Washington, House Republicans were demanding that the Senate negotiate their demand for a one-year delay in making millions of people buy health insurance under President Barack Obama's 2010 health care law.
Minutes before midnight, the White House ordered a shutdown.
The Democratic Senate on Monday twice rejected Republican demands to delay key portions of what has become known as Obamacare as a condition for keeping the government open.
An estimated 800,000 federal workers faced enforced absences, although many were told to work a half-day on Tuesday.
Critical functions such as air traffic control and military operations will continue. Social Security benefits will be paid. National parks and most federal offices will close.
Mr Obama told members of the military he would work to get Congress to re-open the government as soon as possible.
The president addressed troops in a video message after Congress missed the midnight deadline.
Mr Obama said troops in uniform would remain on duty as usual. He said he had signed a law ensuring troops get paid on time.
He said ongoing operations in Afghanistan and elsewhere would continue and the US would ensure those in harm's way would have what they need.
But he said Defence Department civilians may face enforced absences.
As Congress gridlocked, Mr Obama said a "shutdown will have a very real economic impact on real people, right away," with hundreds of thousands of federal workers facing enforced absences and veterans' centres, national parks, most of the space agency and other government operations shuttered.
He laid the blame at the feet of House Republicans, whom he accused of seeking to tie government funding to ideological demands, "all to save face after making some impossible promises to the extreme right wing of their party".
House Speaker John Boehner responded a short while later on the House floor. "The American people don't want a shutdown and neither do I," he said. Yet, he added, the new health care law "is having a devastating impact. ... Something has to be done".
The stock market dropped on fears that political gridlock between the White House and a Republican Party influenced by hardcore conservative tea party lawmakers would prevail, though analysts suggested significant damage to the national economy was unlikely unless a shutdown lasted more than a few days.
A few minutes before midnight, White House Budget Director Sylvia Burwell issued a directive to federal agencies to "execute plans for an orderly shutdown".
The State Department will continue processing foreign applications for visas, and embassies and consulates overseas will continue to provide services to American citizens.
Any interruption in federal funding would send divided government into territory unexplored in nearly two decades. Then, Republicans suffered grievous political damage and President Bill Clinton benefited from twin shutdowns in 1995 and 1996. Now, some Republicans said they feared a similar outcome.
If nothing else, some Republicans also conceded it was impossible to use funding legislation to squeeze concessions from the White House on health care. "We can't win," said Senator John McCain, the 2008 Republican presidential candidate.
On a long day and night in the Capitol, the Senate torpedoed one Republican attempt to tie government financing to changes in the health care law, referred to as Obamacare. House Republicans countered with a second despite unmistakable signs their unity was fraying - and Senate Democrats promptly rejected it, as well.
Defiant still, House Republicans decided to re-pass their earlier measure and simultaneously request negotiations with the Senate on a compromise. Some aides conceded the move was largely designed to make sure that the formal paperwork was on the Senate's doorstep as the day ended.
Whatever its intent, Senate Majority Leader Harry Reid rejected it. "That closes government. They want to close government," he said of House Republicans.
As lawmakers squabbled, Mr Obama spoke bluntly about House Republicans. "You don't get to extract a ransom for doing your job, for doing what you're supposed to be doing anyway, or just because there's a law there that you don't like," he said. Speaking of the health care law that undergoes a major expansion on Tuesday, he said emphatically: "That funding is already in place. You can't shut it down."