Updated: 8:40 p.m.

President Barack Obama issued an ultimatum Friday to Congressional leaders to present him with a plan to avoid a government default just moments after Speaker John Boehner (R-Ohio) pulled out of debt talks yet again over an impasse on revenues.

Obama has summoned Boehner, Minority Leader Nancy Pelosi (D-Calif.), Senate Majority Leader Harry Reid (D-Nev.) and Senate Minority Leader Mitch McConnell (R-Ky.) to the White House for an 11 a.m. Saturday meeting in a scrambled effort to find a way to clear a bill through Congress that would extend the debt ceiling through 2013 before the Treasury’s Aug. 2 deadline.

But it clearly hasn’t, and won’t, be easy. And time is running out. Even top Republican aides conceded that Congressional leaders will need to come up with a framework to present to their Conferences by Monday in order to have enough space to gin up support and go through the procedural red tape required to raise the nation’s debt limit.

All parties Friday — especially the president — demonstrated a new level of frustration at yet another impasse. Boehner cited revenues as the root of the second collapse of talks between him and Obama, while Obama asked of Republicans in aggravation, “Can they say yes to anything?”

“We have run out of time,” Obama said, noting that he “expects answers” Saturday from the leaders. “They are going to have to explain to me how it is that we are going to avoid default.”

Obama was particularly harsh on House Republicans, saying they have “left [him] at the altar a couple times” and that he believes he offered them “an extraordinarily fair deal.”

Both Democratic and Republican sources confirmed Friday that the ongoing talks between Boehner and Obama would have resulted in $3 trillion to $3.5 trillion in savings over 10 years, $300 billion in Medicare cuts, $125 billion in Medicaid reform and substantial Social Security reform.

But the GOP was telling a different story, with the Speaker insisting that Obama “refused to get serious” about entitlement spending. Boehner said the president had “demanded $400 billion more” in the form of raising taxes on businesses that create jobs, and “that’s the bottom line.” He again likened negotiations with Obama to speaking with “Jell-o” and accused the White House of “moving the goal post.”

Republican aides said that the administration had insisted on a higher revenue threshold — “They pulled back after the ‘gang of six’ plan was unveiled,” said one GOP aide of the White House — and a “dialed-back” approach to dealing with Social Security.

In a reprise of his late Saturday evening pullout from talks two weeks ago, Boehner suddenly announced Friday evening he was again walking away from debt limit negotiations, distributing a letter to his Members and calling Obama and both Senate leaders to inform them of his decision.

After a week of reported momentum, Boehner said talks with Obama were not nearly as productive as would have been necessary to strike a sweeping deal.

“A deal was never reached, and was never really close,” Boehner wrote in a “Dear Colleague” letter distributed Friday evening to his Conference. “The president is emphatic that taxes have to be raised.”

“The president is adamant that we cannot make fundamental changes to our entitlement programs,” Boehner’s letter continued. “For these reasons I have decided to end discussions with the White House and begin conversations with the leaders of the Senate in an effort to find a path forward.”

Boehner phoned Obama around 5:30 p.m. to inform him he was stepping away from the talks. In his briefing with reporters, Obama said he “couldn’t get a phone call returned” all day from the Speaker.

A White House official told Roll Call that Obama had tried twice to reach Boehner — once Thursday night and again during the day Friday. The president’s message was that the group was “very close” to a deal and that he was “open” to an agreement, the official said.

The official also said that one sticking point was over Obama’s health care law, with Republicans wanting to write in a repeal of the individual mandate, something that Obama believed was a “totally extraneous” issue and a “non-starter.”

Boehner’s characterization that the president was unwilling to budge on entitlements, however, did not seem to jive with the numbers released by both sides about changes Obama had put on the table for Medicare, Medicaid and Social Security. And an aide close to the “gang of six,” pushed back immediately on the Republican charge that the dynamics of the group had altered the conversation. “Boehner has been briefed on this from the start and knew what was coming on Tuesday and what to expect with the Gang,” the aide said, citing constant conversations between the Republican leader and close friend Sen. Saxby Chambliss (R-Ga.) since April.

Boehner had been working since last week with the Obama administration, beginning with a meeting last Friday with Treasury Secretary Timothy Geithner and White House Chief of Staff William Daley, to close in on a “grand bargain” worth $3 trillion to $3.5 trillion, GOP aides said.

GOP aides said that Boehner and the White House were settling on a tax reform revenue ceiling of $36.2 trillion over 10 years, with agreement on principals attached to the reform in the individual side in three rates, with the top rate being less than it was in 2011. The aides indicated that the White House then wanted a “higher revenue target, not a ceiling” after Tuesday’s unveiling of the bipartisan gang of six plan, which included higher revenues than being negotiated and had been garnering GOP support.

Another sticking point had been the trigger to raise the debt ceiling for a second time, as the framework being negotiated was a “two-step process” that would extend the debt ceiling through February or March, leaving “requisite time” for committees to work on legislation to generate more deficit reduction, according to the aides. The first step would have raised the limit, imposed discretionary caps and installed a reconciliation-like process between the two chambers. Republican aides say Obama did not want the second date alone to be the “default position” trigger, so both sides sought to create an “equal political position.”

The Democrats would have gotten a de-coupling of the Bush Era tax cuts, making more permanent the breaks for the middle class and the Republicans asked for a repeal of the individual mandate provision in Obama’s health care law in the case that the two sides failed to hold up their end of the deficit reduction bargain in the future, aides said.

Now the Ohio Republican, still tethered by a conservative caucus with many Members unwilling to raise the debt limit under any circumstance, will begin work with McConnell and Reid to try to find an acceptable way to extend the nation’s credit. McConnell and Reid met in the Minority Leader’s office earlier Friday and have been working on a so-called Plan B for weeks in the event that a larger deal cannot be reached.

The Reid-McConnell framework would raise the debt ceiling in a series of three votes through the 2012 elections, ask the president to make suggestions for cuts and establish a joint commission to produce a report by the end of the calendar year on a larger plan to tackle the debt. House Republicans have expressed reservations that the plan cedes too much power to Obama by giving him the primary responsibility in raising the debt ceiling, and GOP leadership has been quietly meeting for much of the week to work out options of their own. Meanwhile, Senators on both sides of the aisle have indicated an openness to move forward with the plan.

The Senate has adjourned for the weekend, but leaders could begin the process of bringing a bill to the floor as soon as it reopens, though House Republican aides would not say that they have the votes to move the Reid-McConnell framework through their chamber. House Democratic aides, however, seemed to indicate their bosses were lining up behind the deal.

In his brief session with reporters Friday night, Obama was asked if he was confident the group would strike a deal.

“Yes,” he said, because, “I cannot believe that Congress would end up being that irresponsible that they would not send a package that avoids a self-inflicted wound to the economy at a time when things are so difficult.”

Christina Bellantoni contributed to this report.