"The government is closed because of the irrationality of what's going on on the other side of the Capitol," said Senate Majority Leader Harry Reid.
In addition to "closed" signs and barricades springing up at the Lincoln Memorial and other tourist attractions, NASA and the Environmental Protection Agency were virtually shuttered, and Obama said veterans centers would be shut down.
Government workers classified as essential, such as air traffic controllers, Border Patrol agents and most food inspectors, remained on the job.
So, too, members of the military, whose pay was exempted from the shutdown in separate legislation Obama signed late Monday. Employees whose work is financed through fees, including those who issue passports and visas, also continued to work. The self-funded Postal Service remained in operation, and officials said the government will continue to pay Social Security benefits and Medicare and Medicaid fees to doctors on time.
At the White House, aides discussed whether Obama should change plans for a trip to Asia scheduled to begin Saturday. Staffing was reduced at the famed mansion, where a groundskeeper working outside at daybreak said he was doing the work normally handled by four.
In Congress, some aides were furloughed and others said they were working without pay. 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 for all of them.
Associated Press writers Lauran Neergaard, Alan Fram, Josh Lederman, Nedra Pickler, Seth Borenstein and Andrew Taylor contributed to this report.