Congressional leaders and the White House are nearing a deal on a two-year budget agreement that would increase military and domestic spending in exchange for long-term spending cuts to programs like Social Security and Medicare.

The legislation would also likely be paired with an increase in the federal borrowing limit through March 2017, preventing a potentially disastrous default next week.

The time frames laid out in the potential deal would also effectively ensure the end to the near constant budget and debt limit fights that have dominated President Obama’s relationship with congressional Republicans by pushing the next set of fiscal deadlines into 2017 when the White House will have a new occupant.

The outline of agreement was being presented to members late on Monday and aides cautioned nothing was final as details are ironed out and leaders gauge the support from  rank-and-file members. Still, the talks could potentially mark the first big breakthrough in budget discussions since the 2011 accord between Rep. Paul Ryan (R-Wis.) and Sen. Patty Murray (D-Wash.), which increased the budget caps above the so-called sequester levels.

House Speaker John A. Boehner (R-Ohio) led the negotiations with the White House. He intends to step down from the speakership by Friday, and a deal would not only give him a real accomplishment on his way to the exits but also absolve Ryan, the speaker-in-waiting, from having to deal with imminent debt limit and budget problems.

But it’s unclear whether House conservatives will support the deal, or even whether it can get through the Senate.

Senate Majority Leader Mitch McConnell (R-Ky.) “is going to talk to members of our conference and sort of test the waters and see where we go from there,” Senate Majority Whip John Cornyn (R-Texas) told reporters Monday afternoon.

House Rules Committee Chairman Pete Sessions (R-Texas) said he expects his committee to discuss the agreement soon. He said spending increases proposed in the deal would be entirely paid for though spending cuts and other savings.

Asked if Ryan participated in the talks, Sessions said the deal was arranged and negotiated by Boehner and would be finalized by Boehner.

“In my opinion Paul will be responsible for things when Paul becomes speaker,” Sessions said. “Paul is not responsible for this.”

McConnell has repeatedly said that he will wait to see what the House can pass before embracing any plans.

“As the details come in and especially if an agreement is reached, I intend to consult and discuss the details with our colleagues,” McConnell said on the Senate floor Monday.

White House Spokesman Josh Earnest told reporters that the deal is not final.

“Not everything has been agreed to,” he said. “That means that nothing at this point has been agreed to.”

The timeline is tight for building support for the plan with the Treasury Department saying the debt ceiling will be hit by Nov. 3.

Boehner presented details of the deal, which is expected to include equal increases in both domestic and military spending, to his conference late on Monday.

Republican Study Committee Chairman Bill Flores (R-Texas) said the mood in the meeting was “mildly positive,” but members are waiting to hear the full details of the deal.

“It was better than I expected,” Flores said. “I’m not going to say it was ebullient and it wasn’t dour.”

But some conservatives criticized the deal.

“I would say that we’re very skeptical at this point,” said John Fleming (R-La.). He added that some members, including Budget Committee Chairman Tom Price (R-Ga.), confronted Boehner at the meeting for going around committee chairs.

“He threw the committee chairmen under the bus,” Fleming said.

The tentative deal was the result of weeks of negotiations between Boehner, McConnell, House Minority Leader Nancy Pelosi (D-Calif.), Senate Minority Leader Harry Reid (D-Nev.) and the White House. Leaders hoped to finalize the agreement as early as Monday night, setting up a vote in the House as early as Wednesday, according to a source familiar with the negotiations.

The agreement would include about $80 billion more in spending over two years for defense and domestic programs, which would be offset by savings from changes to the Social Security Disability Insurance fund and Medicare payments to doctors and other health care providers. It also includes an additional $16 billion over two years from off-budget spending increases from the Overseas Contingency Operations Fund. That portion would not need to be offset, but Democrats previously opposed using the money for defense-only spending. In addition, a premium increase for Medicare Part B recipients would be prevented from going into effect.

The proposal being negotiated would set the top-line spending numbers and give the House and Senate Appropriations Committees until Dec. 11 to decide how it should be parceled out among federal agencies and programs.

In addition, the deal would extend the sequester budget caps through 2025, leaving lawmakers to renegotiate spending plans in 2017 if they hope to avoid deep cuts to mandatory spending programs in the future.

Some House Republicans questioned whether the savings achieved over time would be worth allowing an increase in spending now.

“I can’t vote for something where we spend the money today and save it 10 years from now,” said Rep. Lynn Westmoreland (R-Ga.). “That to me is crazy.”

The deal would be one of the very last items negotiated by Boehner before he steps down at the end of the week. He is under pressure to secure a deal before he leaves, so that Ryan will not have to begin his speakership by dealing with a contentious budget fight.

But conservatives will be closely watching whether Ryan supports the deal and works to get it enacted, particularly since it was negotiated by leaders and did not go through the relevante committees.

“I hope Paul Ryan will let us know how he feels about the process,” Rep. Justin Amash (R-Mich.) said.

To help offset the cost of the discretionary spending increases, aides said the deal also would likely include new rules for the Social Security Disability Insurance fund, which is expected to run out of funds by the end of 2016. Discussions have also included maintaining a 2 percent cut to Medicare provider payments that were included in the 2011 Budget Control Act, also known as the sequester.  Those cuts could be problematic for Democrats who have insisted that there be no changes to Medicare or Social Security in a budget deal.

The deal under discussion would extend the life of the disability fund for as many as six years and would include programmatic changes, such as allowing some recipients who can still work to take partial payments while earning outside income. The plan would avoid across-the-board disability insurance cuts by implementing smaller changes like expanding a program requiring a second medical expert to weigh in on whether or not an applicant is truly disabled.

A pilot version of that program has been in effect in several states and has been shown to reduce the number of applicants approved, lowering the cost of the program. Other savings would come from so-called “good governance” changes that are intended weed out waste and fraud.

Mike DeBonis contributed to this story.