He told reporters at the White House that lawmakers should think "long and hard about what's at stake" before the bill goes to the Senate next week.
Mr Obama has been touring the US in recent weeks to promote his $447bn (£290bn) American Jobs Act.
Republicans reject a proposed tax rise on wealthier people to pay for it.
Mr Obama told Thursday's news conference he would support a new approach by Senate Democrats to pay for the act with a tax on millionaires, rather than his plan to raise taxes on couples making more than $250,000.
'Not a game'A tough-talking Mr Obama warned that if Congress failed to act, "the American people will run them out of town".
Continue reading the main storyIf the goal is to create jobs, then why are we even talking about tax hikes?”End Quote Mitch McConnell Republican Senate leader "This is not a game," he warned lawmakers.
Mr Obama cited independent experts as having told him that the act could spur 2% in economic growth and create up to 1.9m jobs.
"Any senator out there who's thinking about voting against this jobs bill when it comes up for a vote needs to explain exactly why they would oppose something we know would improve our economic situation at such an urgent time," he said.
Touting the bill as an "insurance policy" against a new recession, the president said Europe's debt crisis was the biggest threat to the US economy, which he said "really needs a jolt right now".
Mr Obama challenged Republicans on their opposition to a plan that he said would create jobs and rebuild US highways, bridges and schools.
But such new stimulus spending is one reason why Republicans have rejected much of the jobs initiative, together with the proposals for tax increases on wealthier people and small businesses.
Long queues at jobs fairs, like this one in Washington state, have become a common sight Republicans in the House of Representatives have passed a number of bills as part of their own job-creation agenda.
Their legislation has included proposals to loosen pollution regulations and make it easier to drill for oil and gas. But none of the measures has been taken up for a vote by the Democratic-controlled Senate.
On Thursday, Mr Obama defended his decision to criticise Republicans, sometimes by name.
"I think it's fair to say that I have gone out of my way in every instance - sometimes at my own political peril and to the frustration of Democrats - to work with Republicans to find common ground to move this country forward," he said.
He added: "Each time, what we've seen is games-playing, a preference to try to score political points rather than actually get something done on the part of the other side."
But the president's speech on Thursday did little to impress Capitol Hill Republicans.
"If the goal is to create jobs, then why are we even talking about tax hikes?" Republican Senate Minority leader Mitch McConnell said on Thursday.
House Speaker John Boehner, meanwhile, said Mr Obama had "given up on the country" to focus on his re-election.
US unemployment remains jammed at 9.1%, and analysts expect data on Friday to show only modest job growth.
