 "Obama makes little headway with Republicans over deficit")
"If the president wants to let our unwillingness to raise taxes get in the way, then we're not going to be able to set differences aside and focus on what we agree on," House Majority Leader Eric Cantor, the No. 2 House Republican, told reporters shortly after the meeting in the basement of the Capitol.
Earlier in the day, Obama also tamped down expectations for a major deal soon to shrink the deficit.
"Ultimately, it may be that the differences are just too wide," the Democratic president told ABC television.
House Speaker John Boehner, the top elected Republican in the United States, agreed that wide differences remain, even after Obama's strong re-election victory last November.
Boehner did not restrain his criticism following Wednesday's meeting, telling reporters: "Republicans want to balance the budget. The president doesn't. Republicans want to solve our long-term debt problem. The president doesn't. We want to unlock our energy resources to put more Americans back to work. The president doesn't."
Nonetheless, Obama and Republicans in Congress have left the door open to continuing to search for ways to shave hundreds of billions of dollars, or even trillions, from long-term deficits.
A White House official, who asked not to be identified, said Obama told Republicans that since he no longer needs to seek re-election, he is able to focus more freely on what he can get done on issues ranging from the budget to gun violence, immigration reform and cyber security.
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Several Republicans left their meeting with Obama telling reporters that the president said he was willing to wring budget savings out of "entitlement" programs, which include Medicare and Medicaid healthcare for the elderly, disabled and poor.
While that would be a significant step toward Republicans, if Obama followed through, House Republicans were apparently unwilling to make any steps toward Obama on tax increases. They have argued that Democrats won more than $600 billion in tax hikes on the rich at the beginning of this year. That, coupled with new taxes related to Obama's healthcare law, are enough, they argue.
Republicans took control of the House in 2011, two years after Obama became president, and have been a thorn in his side ever since.
Conservative House Republicans, many of them Tea Party activists, at various points have pushed for government shutdowns and a first-ever default on US debt in their drive to get Obama to agree to significantly shrink the size of the federal government and budget deficits.
Despite their contentious relations, a smiling Obama left the 90-minute, closed-door meeting with House Republicans telling reporters, "I enjoyed it. It was useful."
But there were no pictures of Obama and House of Representatives Speaker John Boehner walking together, as Boehner trailed the president when the two exited.
Competing visions
But as the House Budget Committee worked to approve Chairman Paul Ryan's 10-year budget plan later in the night, Republicans kept hammering Obama on his refusal to embrace that document's goal of erasing all deficits by 2023.
"It's disappointing to hear he doesn't believe we need to balance the budget within a 10-year time frame," Representative Greg Walden of Oregon told reporters.
Obama has said he is more focused on seeing a budget that helps create jobs and spurs the US economy.
House Ways and Means Committee Chairman Dave Camp said Obama did inform them that he "wanted revenue-neutral corporate tax reform. So that was a very major point." If that is the case and Obama simultaneously sticks to his goal of raising more tax revenue for deficit-reduction, the burden would likely fall more heavily on high-income earners.
Republicans also peppered Obama with questions about the $85 billion in automatic spending cuts, known as "sequestration," that went into effect March 1 and have been a months-long source of tension between Congress and the White House.
Representative Darrell Issa of California, said one fellow Republican asked Obama why "they closed down the White House (to public tours) rather than canceling the congressional Christmas party" in order to achieve some of the required savings.
As Obama visited House Republicans - he will return on Thursday to meet with House Democrats - the Senate Budget Committee, run by Democratic Senator Patty Murray, began debating its counter-proposal to the Ryan budget.
That plan would cut US deficits by around $1.85 trillion over 10 years with an equal mix of spending cuts and tax increases on the wealthy and corporations.
Annual US deficits under her plan would hover in the $400 billion-$600 billion range for much of the next decade. But Democrats argue that this would allow for stronger near-term job growth than Republicans' balanced-budget vision.
Full details of the plan released by Murray on Wednesday showed that deficits would average 2.4% US economic output through 2023, a level that many economists view as sustainable.
The Ryan budget would see an average deficit-to-GDP ratio of 0.6%. It is currently at 5.6%.
In recent years, agreement on a budget resolution - which is supposed to broadly set out the government's spending priorities - has been the exception rather than the rule. The last time one passed Congress was April, 2009, when Democrats controlled both chambers of Congress and the White House.
But Obama and some Republicans have raised hopes that this year might be different, with Obama's new outreach to Capitol Hill raising expectations.
If the full House and Senate pass their competing budget blueprints next week, which is a possibility, that could set the stage for an intensive negotiation toward a compromise over the next few months.