Obama readied a midday statement to the nation while Democrats and Republicans at the Capitol blamed each other for the first shutdown in nearly two decades.
"Closed" signs and barricades sprang up early Tuesday at the Lincoln Memorial, and national parks and many federal workplaces across the country followed suit. Agencies like NASA and the Environmental Protection Agency were virtually shuttered.
But people classified as essential government employees -- such as air traffic controllers, Border Patrol agents and most food inspectors -- will continue to work. So will members of the military and employees whose jobs are financed through fees, such as State Department workers who issue passports and visas.
With the Republican-controlled House and Democratic-controlled Senate stalemated, it was unclear how long the shutdown -- and the loss of some government programs and services -- could last. The Senate early Tuesday rejected the House's call to form a negotiating committee to resolve the deadlock.
Moments after the vote, Senate Majority Leader Harry Reid, D-Nev., laid full blame on House Republicans, declaring, "The government is closed because of the irrationality of what's going on on the other side of the Capitol."
But Republican Sen. John Cornyn of Texas said GOP lawmakers were listening to constituents who want to "stop the runaway train called the federal government." Their message, he said, is "Stay strong."
Obama communications director Jennifer Palmieri told MSNBC that the White House was open to changes in the health care law in future negotiations, but not as part of passing a budget bill. She compared that to negotiating with "a gun pointed to your head."
Obama was meeting with citizens signing up for his health care program on the opening day of enrollment. Then he planned to make a statement about the shutdown in a lunch-hour speech in the Rose Garden.
In the House, conservative Rep. Marsha Blackburn predicted the standoff might drag on for days if Obama and Senate Democrats refused to bargain. "People are going to realize they can live with a lot less government," Blackburn, R-Tenn., told Fox News.
Another Republican, Rep. Scott Rigell of Virginia, whose Norfolk-area district includes tens of thousands of military members and their families, tweeted "We fought the good fight. Time for a clean CR" -- referring to a continuing resolution that would reopen the government without addressing health care.
The health care law itself was unaffected Tuesday as enrollment opened for millions of people shopping for medical insurance.
It was the first shutdown since a budget battle between Republicans in Congress and Democratic President Bill Clinton in the winter of 1995-1996.
Congress itself was affected. Some staffers were furloughed and hearings were postponed. The U.S. Capitol canceled tours not personally led by lawmakers. Democratic Sen. Tom Carper sent an email to his Delaware constituents telling them not to expect responses to their emails and phone calls.
Lawmakers and the president were still getting paid, however, at a rate totaling more than $250,000 per day. Most of the nation's 2.1 million civilian federal workers were either working with their pay suspended or on unpaid furlough.
The Supreme Court operated as usual, even welcoming tour groups, but was at risk of running low on money if the shutdown lingers beyond Friday.
Tourists were left with few other government options. The Smithsonian website displayed a red banner noting that "all Smithsonian museums and the National Zoo are closed." On the zoo's website, panda mom Mei Xiang could be seen snuggling with her weeks-old cub through the morning, until the feed was abruptly cut off around 8 a.m. Care of the animals will continue behind the scenes.
The White House was operating with a skeletal staff, including household workers taking care of the first family's residence and presidential aides working in the West Wing. A groundskeeper working outside Tuesday morning at daybreak said he was doing the job normally handled by four workers.
Given the shutdown, White House officials were discussing whether President Barack Obama should change plans for a trip to Asia scheduled to begin Saturday.
The military will be paid under legislation freshly signed by Obama, but paychecks for other federal workers will be withheld until the impasse is broken. Federal workers were told to report to their jobs for a half-day but to perform only shutdown tasks like changing email greetings and closing down agencies' Internet sites.
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.
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. Early Tuesday the House named negotiators for what would be a Senate-House conference to work out differences on the bill. The Senate rejected that gambit.
As the standoff continued, some Republicans voiced nervousness.
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.
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.
The spending bill at the center of the fight would fund the government only through Nov. 15 if the Senate gets its way or until Dec. 15 if the House does -- and even an agreement to reopen government temporarily might do little to fix the underlying standoff.
House Speaker John Boehner had sought to avoid the shutdown and engineer passage of a "clean" temporary spending bill. But 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, even as the party moved forward with the plan. 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.
Take ABC13 with you!
Download our free apps for iPhone, iPad, and Android devices