Speaker of the House John Boehner updated the House on “fiscal cliff” negotiations Tuesday, saying “the American people have to be scratching their heads,” as to what President Obama is thinking. (The Washington Post)

President Obama and House Speaker John A. Boehner were struggling late Tuesday to prevent negotiations from breaking down after they traded dueling proposals for averting the year-end “fiscal cliff” that made no progress toward an agreement.

Obama telephoned Boehner (R-Ohio) on Tuesday, hours after receiving the speaker’s latest proposal for a deal on taxes and spending. The offer was virtually identical to the document Obama summarily rejected just one week ago, according to Republican aides.

Obama’s chief negotiator, Rob Nabors, later rushed to the Capitol to meet with Boehner’s top aides.

Even as Boehner spokesman Michael Steel announced that a new offer had been delivered to the White House, he complained that Republicans are “still waiting” for Obama to propose serious cuts to popular health and retirement programs that are forecast to swell the national debt in coming decades.

“Where are the president’s spending cuts?” Boehner asked earlier in the day in a speech on the House floor. “The longer the White House slow-walks this process, the closer our economy gets to the fiscal cliff.”

The Washington Post’s Chris Cillizza looks at the potential dealmakers in the “fiscal cliff” talks. (The Washington Post)

White House officials, meanwhile, complained that they were still waiting for Republicans to produce an offer that includes higher tax rates for the wealthy, a major focus of Obama’s victorious reelection campaign.

“There is a deal out there that’s possible, and we do believe that the parameters of a compromise are pretty clear,” said White House press secretary Jay Carney. “What is required is agreement by Republicans to some specific revenues that includes raising rates on the highest earners.”

The sniping comes just three weeks before nearly $500 billion in automatic tax hikes and spending cuts are set to take effect, potentially triggering a new recession. Earlier in the week, negotiations appeared to be intensifying as Boehner visited the White House on Sunday for his first solo meeting with Obama since the November election.

Boehner described that meeting as “cordial,” and senior GOP aides said they were left with the impression that the president was willing to reduce his demand for $1.6 trillion in new taxes over the next decade to $1.2 trillion. The aides viewed that as an improvement, though still too high for GOP leaders to accept.

But on Monday, matters deteriorated when administration officials delivered a formal offer that Republicans said included $1.4 trillion in new taxes. A person close to the talks said the White House also offered to undertake an overhaul of the corporate tax code, a goal of both parties that is particularly important to the GOP. Still, in the Republicans’ view, the higher revenue figure was a significant step backward.

Republicans fired back Tuesday with a counterproposal that Steel said “would achieve tax and entitlement reform to solve our looming debt crisis.”

Neither the White House nor Republican leadership aides would provide details of the latest GOP plan, but Republican sources close to the talks said the offer made no concessions on the central issue of higher tax rates for the wealthy.

In their initial offer last week, Boehner and other House leaders offered to raise $800 billion in new revenue over the next decade. They insist that the cash should come entirely from scaling back deductions, not from raising rates, which they argue would hurt business and stifle job creation.

Boehner and the White House are also far apart on the scope of spending cuts. Republicans are demanding $600 billion in savings from federal health programs and another $600 billion in other cuts. They also want about $200 billion from applying a less-generous measure of inflation to the tax code and Social Security.

The White House, in its initial proposal two weeks ago, offered $600 billion in spending cuts. A little more than half — $350 billion — would come from health programs while the rest would come from other automatic spending programs, such as farm subsidies.

On Tuesday, Obama said in an interview with ABC News that he remains open to additional policies, such as raising the Medicare eligibility age from 65 to 67.

“When you look at the evidence, it’s not clear that it actually saves a lot of money,” he said. “But what I’ve said is, let’s look at every avenue, because what is true is we need to strengthen Social Security, we need to strengthen Medicare for future generations.”

Still, senior Republicans echoed Boehner’s criticism that Obama’s offer would do too little to cut spending. White House officials bristled at the charge.

“If there is one fact that should not be in dispute it ought to be this: The President, unlike any other party to these negotiations, has put forward detailed spending cuts as well as detailed revenue proposals,” Carney told reporters.

Carney acknowledged that the White House, since its initial offer, has backed away from a portion of its plan to reduce health-care spending, a proposal to shift Medicaid costs onto the states. That step would save about $18 billion over the next decade, according to the nonpartisan Congressional Budget Office.

But Carney called it “a very small percentage of the provisions in here” and said the administration “would absolutely make [it] up” in other ways.

Amid the day’s sparring, Senate Majority Leader Harry M. Reid (D-Nev.) lamented that it now appears “extremely difficult to get [a deal] done before Christmas.”

“We can do things very quickly,” he told reporters, “but this is not something we can do easily.”