Updated: 10:45 p.m.

President Barack Obama announced Sunday evening that after weeks of failed attempts, partisan fights and market trepidation, he and Congressional leaders had reached a deal to avert government default and reduce the deficit by $3 trillion over the next 10 years.

The White House and top lawmakers agreed to a two-step approach to reaching their savings target. The package’s significant guaranteed spending cuts and lack of immediate tax increases appeared to give Republicans most of what they were seeking, but GOP leaders did back off on their insistence that it raise the debt limit in increments. The immediate increase of about $2.4 trillion would last the nation through the 2012 elections, which had been one of Obama’s top demands.

“Is this the deal I would have preferred? No,” Obama said in remarks from the White House briefing room, but it will “allow us to avoid default and end the crisis Washington imposed on the rest of America.”

Just because the principals have agreed, however, does not mean the battle to extend America’s borrowing capacity and to strike a deficit reduction deal is over. Even Obama conceded, “We’re not done yet,” issuing a call from the podium to Washington’s rank-and-file lawmakers for their support, even if they, too, are displeased with portions of the agreement.

On a conference call with his caucus that began mere minutes before Obama spoke, Speaker John Boehner (R-Ohio) sold the deal as a win for Republicans and proof of their influence and their adherence to their principles.

“Since day one of this Congress, we’ve gone toe to toe with the Obama administration and the Democrat-controlled Senate on behalf of our people we were sent here to represent,” Boehner told his Conference, according to his office. “There is nothing in this framework that violates our principles. It’s all spending cuts. The White House bid to raise taxes has been shut down. And as I vowed back in May — when everyone thought I was crazy for saying it — every dollar of debt limit increase will be matched by more than a dollar of spending cuts. And in doing this, we’ve stopping a job-killing national default that none of us wanted.”

At nearly the same time, Senate Majority Leader Harry Reid (D-Nev.) and Minority Leader Mitch McConnell (R-Ky.) took to the floor to announce the compromise and to express confidence that the government would not default on its loans.

“Today, I’m relieved to say that leaders from both parties have come together for the sake of our economy to reach a historic bipartisan compromise that ends this dangerous standoff,” Reid said. “The compromise we have agreed to is remarkable for a number of reasons, not only because of what it does but because of what it prevents: a first-ever default on the full faith and credit of the United States.”

The tone on the floor was a serious shift from just 24 hours prior, when the two leaders sparred intensely over the closeness of a deal and their involvement in making one happen. Reid and McConnell smiled and shook hands Sunday night, knowing they both were driving forces in sealing a deal.

The Senate likely will vote on the deal Monday, as soon as legislative language is pinned down and Conference support is secured, leaving little room for error on the House side to get a bill signed into law before the Treasury Department’s Tuesday default deadline.

Both Senate Democrats and Republicans will hold party caucus meetings Monday morning so leaders can present the final deal to their rank and file. The package won’t completely satisfy either party, but a passage vote in that chamber will be much easier than the lift that House leaders face if the bill advances.

The House Republican and Democratic conferences are expected to meet to discuss the deal Monday afternoon. It’s unclear just how many votes Boehner can deliver, and House Minority Leader Nancy Pelosi (D-Calif.) indicated earlier Sunday evening that many House Democrats may be unwilling to support the deal.

Boehner said he expects to move quickly on the measure if it advances through the Senate.

“My hope would be to file it and have it on the floor as soon as possible. I realize that’s not ideal, and I apologize for it. But after I go through it, you’ll realize it’s pretty much the framework we’ve been operating in,” he said during the conference call Sunday.

Liberals were already wary of the emerging details Sunday, and many will oppose it outright. Rep. Raúl Grijalva, co-chairman of the Congressional Progressive Caucus, said the deal was a disaster for entitlements.

“Progressives have been organizing for months to oppose any scheme that cuts Medicare, Medicaid or Social Security, and it now seems clear that even these bedrock pillars of the American success story are on the chopping block,” the Arizona Democrat said in a statement. “Even if this deal were not as bad as it is, this would be enough for me to fight against its passage.”

Pelosi was reserved in her reaction late Sunday. “We all agree that our nation cannot default on our obligations and that we must honor our nation’s commitments to our seniors, and our men and women in the military,” she said in a statement. “I look forward to reviewing the legislation with my Caucus to see what level of support we can provide.”

The bill cuts would reduce the deficit in two stages, making more than $900 billion in spending cuts in the first stage. In the second stage, a bipartisan joint Congressional committee would identify $1.5 trillion in deficit reduction measures — possibly including revenue raisers and entitlement reform — and make its recommendations by Nov. 23, with Congress acting by Dec. 23. If the committee fails to make its recommendations or Congress fails to enact them, across-the-board spending cuts would be triggered, half of which would come from Defense Department spending. Social Security and Medicaid benefits and veterans’ benefits and pensions would be exempt from these cuts.

The debt ceiling would be raised by at least $2.1 trillion in two steps, with an initial down payment of more than $900 billion followed by an additional $1.2 trillion, which could be triggered by a request from Obama and does not require Congressional approval. The package also requires that both chambers vote on a balanced budget amendment to the Constitution, which would trigger the $1.2 trillion debt ceiling increase if passed.

Jessica Brady, John Stanton Humberto Sanchez contributed to this report.