Updated 3:26 p.m. | Speaker John A. Boehner’s effort to “clean the barn” before leaving Congress is gaining momentum, with the four corners of congressional leadership and the White House hoping for a budget and debt limit deal.  

The Republican from Ohio does not want to leave a crisis behind for Ways and Means Chairman Paul D. Ryan, R-Wis., who is expected to be elected as the new speaker on Thursday.  

Under discussion is a deal that would suspend limits on the nation’s borrowing authority until March 2017, along with two years worth of partial relief from the budget caps known as sequestration. The package would also address the Medicare Part B issue, aimed at protecting millions of seniors from significant increases to their health insurance premiums and deductibles.  

An agreement could be announced as early as Monday evening, according to two familiar with the talks. The House Republican Conference scheduled a meeting for 6 p.m. to discuss the “October agenda,” according to a GOP aide.  

The Treasury Department has said the extraordinary measures used to thwart surpassing the debt limit will be exhausted by early next week.  

White House Press Secretary Josh Earnest told reporters there was no agreement yet, repeating a familiar line from past bipartisan budgetary debates that, “nothing is agreed to until everything is agreed to.”  

Earnest took a hard stance on the White House’s long-held preference that any spending deal avoid boosting Pentagon spending — either in full or in part — by merely inflating its war account known officially as the Overseas Contingency Operations fund. That controversial account is not subject to spending caps, and the White House believes using it in any long-term plan would be an unwise budget “gimmick,” he added, dubbing the practice the “OCO loophole.”  

White House officials for months have said they would not negotiate a debt-ceiling hike, saying the president would only support a “clean” measure to raise it. Earnest batted away a reporter’s question about whether attaching a debt ceiling increase to a long-term budget bill would break the White House’s pledge.  

It “can sometimes be a useful strategy to” attach a debt ceiling-raising measure to some other major legislation that “we know will pass” both chambers and garner the president’s signature, Earnest said, ticking off a list of such instances under several recent presidents.  

A House leadership source said the deal in the works is the outcome of bipartisan sequester negotiations that began on Sept. 17.  

While congressional sources and the White House said the developing agreement could change or fall apart, there was hope for an announcement Monday evening on a debt limit increase that would carry past the 2016 elections and also provide some budget certainty, perhaps for the two years envisioned by Senate Majority Leader Mitch McConnell.  

For the Kentucky Republican, it’s all part of an effort to show that his party can be a functional governing majority ahead of the 2016 election cycle in which GOP incumbents face unfavorable conditions.  

Getting budget numbers in place this week would give a window for House and Senate appropriators to attempt to write a catch-all spending bill ahead of Dec. 11, when the continuing resolution that is temporarily funding the government is set to expire.  

In theory, having agreed upon budget numbers could allow an appropriations process to advance in the next fiscal year, though that may prove impossible for other reasons given the presidential election.  

Rumored offsets for the budget portion of the agreement were already causing heartburn on and off Capitol Hill, with talk of borrowing revenue-raisers from other legislation, such as selling off oil from the Strategic Petroleum Reserve to fund the partial sequester relief.  

And there’s also talk of expanding the use of the overseas contingency operations fund to pay for an increase on the defense side of the ledger.  

Emma Dumain, John T. Bennett, Tamar Hallerman and Paul M. Krawzak contributed to this report.