But by 4 p.m. Sunday — two days before the country would plunge into default — President Barack Obama drew the line against congressional Republicans who wanted assurances that defense spending would be cut less than many other programs.

“We just can’t give there,” Vice President Joe Biden, Obama’s chief emissary to the Hill in the budget negotiations, pointedly told House Speaker John Boehner (R-Ohio).

With that, a grim Obama contemplated the unthinkable: pulling the plug on a deal and precipitating a global economic crisis. Huddled in the Oval Office, the president and his top aides proceeded to discuss how Treasury Secretary Tim Geithner might step out later that night and prepare the country for the inevitable market crash.

Then, almost as abruptly, the compromise started coming together. What happened during a weekend of frenzied negotiations to salvage the deal is a tale of cataclysm narrowly averted, a historic debt-reduction plan that satisfies none of its signatories and a lesson on how even the most dysfunctional political system can be made functional through the injection of fear, finesse and Joe Biden’s old friendships.

With the talks going nowhere Saturday morning, the White House made “our last play,” according to a senior administration official, calling on Biden’s long-time connection to Senate Minority Leader Mitch McConnell (R-Ky.).

“We had tried everything — Boehner talking to Obama, small groups, large groups — and everything fell apart,” the official told POLITICO.

By 4 p.m. Sunday, only one major disagreement remained — and the administration and Democratic congressional leaders would not budge.

After more wrangling, McConnell suggested a solution to the impasse: Redefine “defense” cuts as “security” cuts to include homeland security, veterans affairs and foreign aid, diluting the impact on the Pentagon.

The president called Boehner at 8:15 p.m. to see if that was enough to win over House Republicans.

“Do we have a deal?” he asked.

Boehner interrupted him, and Obama went silent. For a few seconds, the aides assembled around the president waited to see whether this deal, like so many before it, would fall apart.

Then the president spoke up.

“Congratulations to you, too, John.”

This account of the final days of high-stakes negotiations is based on interviews with lawmakers, congressional staff, administration aides and Democratic officials familiar with the talks.

They described an agreement sealed by Obama and Boehner but said it was Biden’s close working relationship with McConnell that broke the months-long logjam.

McConnell and Biden have a long history, serving together for a full 25 years of Biden’s 36-year-tenure as the Democratic senator from Delaware. The two men were at the center of a major tax cut deal in December.

Last Wednesday, Biden and McConnell quietly presented Boehner with a spending-cuts-only package, which Boehner promptly rejected.

McConnell, both a consummate GOP loyalist and old-school dealmaker, then held off Biden for several days before restarting the back-channel talks. He was waiting for Boehner to pass his own debt-limit bill — a measure the Speaker needed to shore up his leadership of the House, but a bill Obama had already promised to veto.

Shortly after lunch on Saturday, McConnell picked up the phone and called Biden to announce he was ready to deal.

The two had never really been out of contact, checking in with each other even as Obama stepped back from direct negotiations with Republicans and the House GOP feuded openly. This time, the stakes were higher and Boehner delegated McConnell as his agent in hopes of streamlining negotiations as the cable networks fired up their doomsday debt clocks.

McConnell wanted to negotiate primarily with Biden, concerned that other Democrats, especially Obama, would prove to be less trustworthy bargaining partners.

“Biden’s the only guy with real negotiating authority, and [McConnell] knows that his word is good,” said a senior GOP staffer close to the talks. “He was a key to the deal.”

The president assigned White House legislative affairs director Rob Nabors to work with Biden. But it was Biden who was tasked with discussing the granular details with McConnell during four phone conversations, narrowing differences over the all-important trigger to be activated if a special bipartisan congressional committee can’t come up with $1.2 trillion more in cuts by November.

Progress was made, but the atmosphere was tense as the hours slipped toward the deadline. By Saturday night, discussions over the trigger had bogged down, and a call between McConnell’s staff and senior White House aides turned heated when GOP negotiators demanded that Medicaid be added to the mix of programs that could face cuts.

Gene Sperling, chairman of Obama’s National Economic Council, was in mid-sentence, trying to calmly explain why the White House wouldn’t allow that, when Office of Management and Budget Director Jack Lew interrupted.

“No!” the typically mild-mannered Lew yelled. “The answer is simply no! No, no!”

The trigger fight dragged on as Obama and aides milled in and out of the spacious West Wing corner office of Bill Daley, Obama’s chief of staff.

Daley played a central role in organizing administration activity but that role diminished as Biden’s grew. He also sparred with Boehner’s chief of staff Barry Jackson over the speaker’s refusal to return Obama’s calls for five hours a week earlier.

“Daley was pissed at Boehner, and they returned the favor,” a congressional Democrat said.

McConnell’s intervention served a dual purpose. He wanted to avoid an economic disaster that would shatter the economy, and possibly his shot at becoming majority leader in 2013. But he was also intent on protecting Boehner, who has been weakened by tea party revolts within in his own ranks — and sought to minimize any daylight between more moderate GOP senators and firebrand House conservatives.

Throughout the day Saturday, the GOP’s odd couple — the fastidious and tight-lipped minority leader and the gregarious, chain-smoking Boehner — held a negotiation-within-a-negotiation as Biden pressed for concessions.

Biden would make a proposal, and McConnell would pad the narrow, red-carpeted hallway behind the rotunda that links his office to Boehner’s, staffers said.

The speaker made the return trip several times himself, standing in shirtsleeves and puffing smoke as McConnell, a non-smoker, listened intently in the impeccable suit some aides suspect he wears 24 hours a day.

Early in the indirect three-way talks, McConnell and Boehner made a critical concession: They ditched their demand for a six-month extension of the debt ceiling and acceded to Obama’s demand that any agreement last through the end of 2012.

But McConnell was enormously sensitive to the perception that he was being rolled — or was straying from Boehner. When Sen. Chuck Schumer (D-N.Y.) went on MSNBC last Wednesday and praised McConnell for proposing a way out of the crisis, the Republican leader approached Senate Majority Leader Harry Reid (D-Nev.) and barked, “Tell your henchman to stop saying nice things about me. … It hurts me.”

On Saturday afternoon Reid and House Minority Leader Nancy Pelosi (D-Calif.) met Obama in the Oval Office, only to hear that the Republicans hadn’t budged on the trigger.

But by Sunday, an agreement on the trigger had been struck at the staff level.

Obama’s final selling job was to his fellow Democrats and here, too, Biden pitched in, according to Democratic aides.

On Sunday night, Democratic leaders — Pelosi, Reid, Schumer, Rep. Steny Hoyer (D-Md.), Sen. Dick Durbin (D-Ill.) and others — gathered around a table in Pelosi’s office to review the details of the deal.

The mood was grim, even testy.

Biden’s argument was ultimately convincing: The trigger contained in the compromise would rely very heavily on automatic cuts to defense programs, anathema to GOP negotiators that might motivate them to consider closing corporate tax loopholes.

“The defense cuts sold them. Basically $800 to $900 billion of the $2.1 trillion is in defense or security cuts,” a senior Democratic aide told POLITICO. “Biden kept saying, that when all things were factored in, it was basically a 50-50 on defense and domestic spending cuts.”

GOP House staffers were burnt out after months of fruitless meetings at the White House that they had taken to calling “joke meetings” or worse still, “Professor Obama’s lectures.”

Moreover, McConnell’s support helped Boehner present the deal as having unified GOP support, key to preserving the party’s leverage in future negotiations with the White House.

To Boehner, the wrangling over a final deal proved far less dramatic than the narrow Friday vote on his own debt-limit bill, a 218-210 victory over Democrats and tea party stalwarts.

Boehner and his whip, Kevin McCarthy, had confronted their own moment of truth the previous Wednesday, when they faced off with about two-dozen tea party conservatives and freshmen who flatly rejected Boehner’s attempt to sell them his version of a balanced budget amendment.

At that moment the leaders and their aides abruptly rose and stomped out of the room — to pleas of “Where are you going?” from the stunned members.

“We’ve heard enough,” one of the staffers replied. Boehner cancelled the vote and tweaked the measure to attract some of the holdouts.

“There was nothing these far-right guys would say yes to,” said a leadership aide close to the talks. “It became clear that they were going to be intransigent no matter what.”

The White House and Hill Democrats derided the ensuing 218-to-200 vote on Friday as a time-wasting exercise in partisan chest-thumping. But for the House GOP leadership it was an absolute necessity — to prove that they could actually whip a tough vote as a team and to identify the number of absolute dead-enders, which shrunk from about 50 to 22 under pressure.

Even though the process was nearly a national disaster, said one GOP aide, “it proved that our engine could actually work … so in that way it was a success.”

Obama did not characterize the deal quite that way when he announced it Sunday night.

“Is this the deal I would have preferred? No,” the president told the nation. “But this compromise does make a serious down payment on the deficit reduction we need and ensures also that we will not face this same kind of crisis in six months or eight months or twelve months.”