WASHINGTON — A North Carolina National Guard infantry battalion called off a training exercise that had been planned for a year. Flu samples from around the country will no longer be collected and tested. A skeleton staff of workers at the Internal Revenue Service girded themselves to answer a deluge of questions about the new tax law.

The vast machinery of the federal government began grinding to a halt on Saturday morning, hours after the Senate failed to reach a funding deal. But like an aircraft carrier after its propellers stop turning, much of the bureaucracy will stay in motion for a while, and some essential services, like the armed forces, the post office and entitlement programs, will not stop working at all.

Tens of thousands of federal workers woke up to notices from their cabinet secretaries informing them that, barring action from Congress, they will be furloughed this coming week. The shutdown is falling unevenly: The Education Department will send home more than 90 percent of its 3,934 employees, while the Pentagon said the entire uniformed military, and half of its civilian work force, would continue to serve. But for now, even the troops will not be paid.

At the White House, three-fifths of President Trump’s staff will be placed on temporary leave. The National Security Council will stay at full strength, but about 60 percent of the president’s closest aides were to be furloughed. Others could come to the White House or telecommute, but only for up to four hours, and only to execute an orderly shutdown.