The U.S. House of Representatives on Tuesday rejected three separate measures that would have funded parts of the federal government shut down since midnight Monday.
The Republican-proposed bills to reopen national parks and museums, fund veterans' services and the city of Washington, DC failed to get the required two-thirds support.
Even if they had passed, the White House said it would veto any partial government reopening.
Spokesman Jay Carney said attempts to fund some operations while leaving others closed shows an utter lack of seriousness.
House Democrats criticized Republicans for worrying about parks instead of programs feeding children. Minority Leader Nancy Pelosi likened it to kidnappers freeing just one hostage at a time.
The government started closing down all but essential services at midnight Monday. The Democratic-controlled Senate rejected spending bills by the Republican-led House that would have delayed or killed President Barack Obama's signature health care program, the Affordable Care Act.
Obama said Republicans are on an "ideological crusade" to kill the measure, known as Obamacare, and criticized their "reckless demands" to deny affordable health insurance to millions of Americans.
He said that closing down the government accomplished nothing because Obamacare is the law of the land, passed by Congress, supported by voters and upheld by the Supreme Court.
Republican opponents of Obamacare say it forces people, including small businesses, to buy expensive insurance policies against their will, hurting the economy.
About 800,000 federal workers are now on furlough. Other federal workers are staying on the job with no guarantee when they will be paid.
The shutdown will not affect Voice of America broadcasts, but it has closed national parks and other services such as federal tax offices, help for veterans, and food aid for the poor. Most civilian employees at the Pentagon must stay home and the U.S. space agency is almost entirely shut down.
The U.S. military will remain on duty, and ongoing military operations like those in Afghanistan will continue.
Experts say a shutdown of more than two weeks is likely to slow the U.S. economy because of reduced tourism and furloughed federal workers cutting back on their spending.