Talks between President Obama and congressional Republicans grew increasingly contentious on Monday, as GOP leaders flatly rejected his call to raise taxes on the wealthy as part of a bipartisan agreement to restrain the nation’s mounting debt.

Dueling news conferences by Obama and House Speaker John A. Boehner (R-Ohio) served as a testy prelude to an afternoon bargaining session that only emphasized the partisan divide, according to people on both sides with knowledge of the closed-door discussions.

During the meeting, Obama challenged Boehner to buck the anti-tax hard-liners in his party, who, the president suggested, are blocking the path to a landmark compromise to reduce borrowing by as much as $4 trillion over the next decade. Boehner and House Majority Leader Eric Cantor (R-Va.) responded by urging Democrats to settle for a more modest reductions-only deal that would save $2.4 trillion but would not touch tax breaks for the nation’s richest households.

In addition to major cuts to domestic agencies, the House GOP proposal calls for slicing about $250 billion from Medicare over the next decade by asking well-off seniors to pay more for health coverage, placing new restrictions on Medigap policies and putting in place new co-payments and cost-sharing provisions for home health care, among other changes. Those reductions would come on top of about $500 billion in Medicare savings previously enacted as part of Obama’s overhaul of the health-care system — cuts Republicans denounced during last fall’s midterm campaign. 

Obama rejected the GOP plan, said a Democratic official familiar with the discussions, arguing that he could not ask “moderate-income seniors to bear $500 or more of additional costs when you couldn’t ask the most well-off American to give an extra $5 to getting the deficit down.”

At a White House news conference hours earlier, a clearly exasperated Obama said he has “bent over backward” to meet Republican demands for sharp cuts in government spending, citing his offer to trim Social Security and Medicare benefits — an offer that has drawn howls from liberal Democrats. That offer included raising the Medicare eligibility age, said the official, who spoke on the condition of anonymity to discuss the talks.

Unless Republicans are willing to make the same ideological concession on taxes, Obama said, “I do not see a path to a deal.”

“We keep on talking about this stuff and we have these high-minded pronouncements about how we’ve got to get control of the deficit and how we owe it to our children and our grandchildren. Well, let’s step up. Let’s do it,” Obama said. “I’m prepared to take significant heat from my party to get something done. And I expect the other side should be willing to do the same thing.”

Republicans fired back that they already are taking plenty of heat for considering an increase in the legal limit on the debt, which stands at a record $14.3 trillion. In a sign of deepening tensions, Boehner suggested that the only concession Obama should expect from Republicans is a vote to allow the Treasury to continue borrowing.

“Most Americans would say that a ‘balanced’ approach is a simple one: The administration gets its debt-limit increase, and the American people get their spending cuts and their reforms,” Boehner told reporters at a news conference before heading to the White House. “Adding tax increases to the equation doesn’t balance anything.”

Obama and Boehner took pains to express their admiration for each other, but the prickly rhetoric suggested that hope has faded for a far-reaching $4 trillion agreement. After a friendly game of golf and three weeks of secret talks, the two had hoped to forge a historic deal to tackle the biggest drivers of the debt, including health-care and retirement programs, military spending and an inefficient tax code.

Boehner blew up those talks last weekend, citing irreconcilable differences with the White House over taxes and the magnitude of structural changes to entitlement programs. “I want to get there,” he said Monday. “But it takes two to tango, and they’re not there yet.”

That sent negotiators back to the drawing board with just three weeks until Aug. 2, when the government risks defaulting on its obligations without additional borrowing authority. Lawmakers in both parties have refused to raise the debt limit without a plan to restrain the debt in the future.

Obama, Vice President Biden, and the top two leaders of both parties in the House and the Senate are racing to draft such a package by July 22, to leave enough time for what is likely to be a difficult sales pitch to their respective rank and file. Negotiators agreed to meet again Tuesday afternoon, and Obama said they will meet daily — including through the weekend, if necessary — to seal a deal.

Monday’s meeting focused on the only apparent alternative to what many have taken to calling the “grand bargain”: A $2.4 trillion package that was under discussion in earlier talks led by Biden.

Cantor, a party to the Biden talks, said the group was tantalizingly close to its target, which would be big enough to permit House Republicans to agree to an increase in the debt limit sufficient to pay the government’s bills until well after the 2012 election.

But Democrats, and some Senate Republicans, said the consensus was closer to $1.5 trillion — and that assumed a deal to raise taxes on wealthy households that the GOP was unwilling to make.

“When Republicans say, ‘Let’s just go back to the Biden talks,’ it’s important to remember, they walked out of the Biden talks,” said Rep. Chris Van Hollen (D-Md.).

Some Republicans have raised the prospect of a short-term deal. But Obama emphatically rejected that option Monday, saying he would not sign “a 30-day or a 60-day or a 90-day extension.”

A deal is only “going to get harder” as the election approaches, Obama said. “So we might as well do it now. Pull off the Band-Aid. Eat our peas.

“If not now, when?”