The self-funded Postal Service will continue to operate and the government will continue to pay Social Security benefits and Medicare and Medicaid fees to doctors on time.
On Capitol Hill, lawmakers get to decide which of their staff members keep working and which are furloughed. Members of Congress will continue getting paid.
There were no "Closed" signs outside the Capitol or its adjacent visitor center early Tuesday warning tourists they would not be admitted for the usual tours. "That would be me," quipped one Capitol Police officer standing outside an entrance.
The Senate twice on Monday rejected House-passed bills that first sought to delay key portions of the 2010 "Obamacare" law, then to delay the law's requirement that millions of people buy medical insurance. The House passed the last version again early Tuesday naming negotiators for a Senate-House conference on the bill; Senate Majority Leader Harry Reid said the same fate awaits that measure when the Senate reconvenes Tuesday morning.
"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," Obama said Monday, delivering a similar message in private phone calls later to Republican House Speaker John Boehner and other lawmakers.
Boehner said he didn't want a government shutdown, but added the health care law "is having a devastating impact. ... Something has to be done."
It wasn't clear how long the standoff would last, but it appeared that Obama and Reid had the upper hand.
"We can't win," said Sen. John McCain, R-Ariz., adding that "sooner or later" the House would have to agree to Democrats' demands for a simple, straightforward funding bill reopening the government.
Another veteran Republican, Rep. Tom Cole of Oklahoma, called the shutdown "a big mistake." Interviewed on MSNBC, Cole called on House and Senate negotiations to end the impasse and insisted Democrats should yield on delaying the requirement that individual Americans have health coverage.
The order directing federal agencies to "execute plans for an orderly shutdown due to the absence of appropriations" was issued by White House Budget Director Sylvia Burwell shortly before midnight Monday.
Around the same time, Obama appeared in a video message assuring members of the military they'll be paid under a law he just signed and telling civilian Defense Department employees that "you and your families deserve better than the dysfunction we're seeing in Congress."
Defense Secretary Chuck Hagel said Tuesday that Pentagon lawyers are trying to determine ways for some of the Defense Department's 400,000 furloughed civilians to continue working.
He bemoaned the standoff, telling reporters traveling with him in South Korea, "It does have an effect on our relationships around the world and it cuts straight to the obvious question: Can you rely on the United States as a reliable partner to fulfill its commitments to its allies?"
The underlying spending bill would fund the government through Nov. 15 if the Senate gets its way or until Dec. 15 if the House does.
Until now, such bills have been routinely passed with bipartisan support, ever since a pair of shutdowns 17 years ago engineered by then-Speaker Newt Gingrich severely damaged Republican election prospects and revived then-President Bill Clinton's political standing.
Boehner had sought to avoid the shutdown and engineer passage of a "clean" temporary spending bill for averting a government shutdown.
This time tea party activists mobilized by freshman Sen. Ted Cruz, R-Texas, mounted a campaign to seize the must-do measure in an effort to derail Obamacare. GOP leaders voiced reservations and many Republican lawmakers predicted it wouldn't work. Some even labeled it "stupid."
But the success of Cruz and other tea party-endorsed conservatives who upset establishment GOP candidates in 2010 and 2012 primaries was a lesson learned for many Republican lawmakers going into next year's election.
Associated Press writer Lolita C. Baldor in Seoul, South Korea, contributed to this report.
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