Obama upped the ante after he met top Republican and Democratic leaders at the White House, warning it would be "inexcusable" not to resolve the standoff this week. Yet his administration has already warned departments to prepare to shutter the government.
"The only question is whether politics or ideology are going to get in the way of preventing a government shutdown," Obama said at an impromptu White House press conference.
A government shutdown could see hundreds of thousands of federal employees furloughed, national parks closed and non-essential services halted when the money approved by Congress for their operations runs out at midnight on Friday.
Shutdowns have unpredictable political consequences and Obama and his Republican foes are playing a high-stakes game with uncertain results.
The last major US government shutdown caused by a political row, in 1995, helped reinvigorate the fortunes of then Democratic president Bill Clinton who was locked in a fierce showdown with a conservative Republican Congress.
Obama's Democrats argue they have already offered $33 billion in cuts from current spending -- a figure Republicans dispute -- but a row is raging over where exactly cuts should be made.
The president, who has ruled out cuts in some spending on education, medical research and on environmental projects, called on all sides in Washington to "act like grownups" saying everybody should give "a little bit" to get a deal.
"It would be inexcusable for us to be not able to take care of last year's business," Obama said.
"What we can't do is have a 'my way or the highway' approach to this problem."
Republicans have made deep spending cuts a bedrock principle of this Congress and included deep trims to expenditures on foreign aid and other domestic programs in legislation that has passed the House.
The situation is complicated by Republicans' control of the House and the Democratic majority in the Senate, meaning a deal must be made before a budget can be endorsed by Congress.
After Obama's remarks, the action shifted back to Capitol Hill and a 40-minute meeting between Senate Democratic Majority Leader Harry Reid and Republican House Speaker John Boehner.
"They agreed to continue working on a budget solution," said Boehner's spokesman Michael Steel.
Obama said that if there was no deal by Wednesday, he would get the two leaders and their negotiating teams back to the White House for more talks.
It was not clear whether he would cancel or delay a planned trip to the Philadelphia area and New York to get back to the negotiating table.
Boehner earlier told reporters there never had been an agreement between the sides on the $33 billion figure and accused the White House of using "smoke and mirrors" accounting to get to the number.
"We've made clear that we're fighting for the largest spending cuts possible," he said.
On the Democratic side, Reid sought to score a political point by suggesting that the Republican leadership in the House was being stretched by the conservative Tea Party movement that wants dramatic spending cuts.
"I'm going to do everything that I can... but I hope the Republicans do what the country needs, not what they believe the Tea Party wants," Reid said.
The Pentagon was closely watching the debate and "engaged in prudent planning" in case of a government shutdown, Pentagon press secretary Geoff Morrell told reporters.
Even with a shutdown, the Pentagon would still be able to fund military operations in Afghanistan, Iraq and Libya as well as humanitarian efforts in Japan, he said.
But it remains unclear whether paychecks would be delayed for service personnel, including the more than 140,000 troops in Afghanistan and Iraq.
The row over last year's budget is Obama's most critical test of will yet with Republicans, who seized the House last year, and it comes with the political world buzzing after Obama launched his reelection bid on Monday.
A current short-term funding measure, which keeps the government open through Friday, is the sixth since the dawn of the 2011 fiscal year.
The Republicans separately unveiled a plan to slash government spending by $6 trillion over the next decade -- setting the stage for a future showdown between the White House and Capitol Hill.
