The Republican-led House of Representatives which had linked passage of a spending bill or a continuing resolution to keep the government running to defunding Obamacare as the healthcare law is nicknamed, instead offered to keep a few popular programmes funded.
The first government closure in nearly 18 years began at the end of fiscal year Oct 1 midnight forcing the administration to furlough close to 800,000 federal workers or about a fourth of government workforce, close national parks and end several non-essential services.
The Republican move to approve piecemeal funding for three popular programmes -- the American capital of Washington in District of Columbia, veterans affairs and national parks -- failed to muster necessary two-thirds majority for passage.
The Republicans plan to bring up the same measures again Wednesday in a way that would require only a simple majority to pass, but Democratic-led Senate is bound to reject it once again. The White House has also promised a veto.
As the stalemate continued, Obama made a television appearance in the White House Rose Garden to publicly admonish the House Republicans to "reopen the government" rather than continue to block federal spending to the 2010 healthcare act.
"As long as I am president, I will not give in to reckless demands by some in the Republican Party to deny affordable health insurance to millions of hard-working Americans," he said flanked by a group of beneficiaries of his Obamacare law.
About 800,000 federal workers furloughed
Saying the shutdown's goal is to hinder government efforts to provide health insurance to 15 percent of the US population that doesn't have coverage, the president said it was "strange that one party would make keeping people uninsured the centrepiece of their agenda".
Senate Majority Leader Harry Reid derided the Republican strategy as "just another wacky idea by tea party Republicans".
Earlier, the Senate began the first day of closure Tuesday by rejecting a Republican plan for a conference committee to work out differences between the two chambers.
Although much of the federal workforce will go without pay, cheques will keep coming to the 533 current members of the Congress. The president too will get paid. His salary -- $400,000 -- is considered mandatory spending.
Members of the military will also get paid -- thanks to the Congress, which unanimously managed to come together to pass a bill that Obama signed.
The influential New York Times blamed the crisis on Republican Speaker John Boehner, saying "The Republicans' reckless obsession with destroying health reform and with wounding the president has been on full display".
"And, as the public's anger grows over this entirely unnecessary crisis, it should be aimed at a party and a speaker that are incapable of governing."
Meanwhile, new healthcare exchanges designed to provide affordable insurance to America's 15 percent uninsured rolled out - the very thing that the Republicans were trying to prevent.
Though initially it faced a plethora of technical glitches, the websites were working fine by the evening with millions of visits to the site.