Speaker John Boehner (R-Ohio) laments the resistance to immigration reform but emphasizes the need for officials to work together. (The Washington Post)

House Republicans return to Washington on Monday still struggling to find a path to raising the Treasury Department’s borrowing authority, but the normally raucous caucus is in unusual agreement that the best option is to put the white-knuckle confrontations of recent fiscal wars behind them.

Facing a timeline that leaves no room for trial and error, some party leaders were advocating a debt-ceiling solution that would wrap several popular, must-pass items around a provision to extend the federal government’s borrowing authority beyond the November midterm elections. That approach has drawn support from some surprising quarters, but several senior GOP advisers made it clear over the weekend that such a proposal would require a bloc of Democratic votes, because about 30 Republicans oppose raising the debt ceiling under any circumstances.

By Sunday night, Republican leaders had not conducted a formal whip tally on their side to determine how many votes they had, and no outreach had been made toward Democrats to determine what kind of support — if any — such a plan would receive from them.

Without as much internal dissent as in previous budget showdowns, Republicans still face a powerful enemy: the calendar. The House will adjourn Wednesday afternoon so Democrats can attend their annual issues retreat on Maryland’s Eastern Shore, and then the entire Congress is shuttered during the week of Presidents’ Day.

Once the chamber closes Wednesday, the House will not return for a full workday until Feb. 26, which is one day before Treasury Secretary Jack Lew has said he will lose his ability to juggle the nation’s finances. The quick march would then begin toward defaulting on portions of the nation’s more than $17 trillion debt, sending global ­financial markets reeling.

This time crunch means that unless Republicans quickly coalesce around a plan, the last week of February will bring another countdown moment before a critical fiscal deadline.

House Republicans are not sounding the confrontational drumbeat of other showdowns with President Obama, who has been adamant that he will accept no trade-offs for what he considers a simple exercise in guaranteeing that the federal government will make good on its debts.

The turn toward compromise signals a break from the tactics used by Republicans in past fiscal negotiations, particularly for those who took the lead in pushing House Speaker John A. Boehner (R-Ohio) into a 16-day shutdown of the federal government in October.

“There is a pragmatism here,” Rep. Michele Bachmann (R-Minn.), who founded the Tea Party Caucus four years ago, said last week. “You’ve got to know when to hold them and when to fold them. My assessment is that most of us don’t think it’s the time to fight.”

Rep. Raúl R. Labrador (R-Idaho), who took part in an aborted coup attempt against Boehner 13 months ago, said, “Our constituents are fed up with the political theater.”

Labrador has gone so far as to advocate turning over the House floor to Democrats and letting them pass a “clean” debt-ceiling hike mostly on their own, foisting political blame entirely on Democrats and raising no false hope among conservative activists that concessions can be wrung from Obama and Senate Democrats.

The attitude of resigned indifference on the debt fight surfaced during the House GOP’s issues retreat two weeks ago, at the same Eastern Shore resort where Democrats will huddle this week. There, according to a handful of Republicans in attendance, a pair of conservative writers — Kimberley A. Strassel of the Wall Street Journal’s editorial page and Ramesh Ponnuru of National Review — urged Republicans to avoid the mistake of a shutdown strategy. Outside conservative groups led the effort last year to compel Obama and Senate Democrats to strip funding for the health-care law, but in the end Republican political standing plummeted, the government was reopened, the debt ceiling was lifted and conservatives got nothing in return.

Most Republicans agree with Strassel and Ponnuru’s viewpoint of avoiding a political pitfall, but Boehner’s leadership team and a wide swath of rank-and-file lawmakers want to get something else out of this debt-ceiling battle rather than just surrendering.

The issue is finding something that can get broad backing from the House GOP but also pick up Democratic support, shifting the onus onto Senate Democrats.

Many Republicans, anxious about the upcoming midterm elections, are urging Boehner to pass legislation that could win bipartisan backing, and the leading options are proposals that Democrats have voiced support for in other negotiations.

A handful of bargaining ideas have emerged, with a proposal to restore recently cut military benefits in exchange for a one-year extension as a leading option. Other ideas, such as tying a debt-limit extension to the “doc fix,” which would alter the way doctors are reimbursed for Medicare treatments, are in the mix.

One idea that gained traction over the weekend would combine the military and Medicare issues with the debt-ceiling extension, along with offsetting cuts that would prolong portions of the automatic spending decreases known as sequestration and changes to pension programs.

But some Republicans are fearful of tying the debt ceiling to the military pension issue, wanting to vote against the debt-limit hike but not wanting to cast a vote that could be portrayed as anti-veteran.

If none of those options gains traction, the fallback plan may well be Labrador’s. House Minority Whip Steny H. Hoyer (D-Md.) has pledged about 180 Democratic votes for a clean debt-ceiling increase, leaving the need for fewer than 40 Republicans to vote with Democrats or to just vote “present” to lower the threshold for reaching the majority.

On Friday, the Treasury began using “extraordinary measures” to buy time before it runs low on cash. The government’s cash on hand is expected to hit $50 billion on Feb. 27, after which Treasury officials fear they could fall short any day.

“If Treasury has insufficient cash on hand, it would be impossible for our nation to meet all of its obligations for the first time in history,” Lew wrote in a letter to Boehner.

In two of the three recent debt battles, Congress did not raise or suspend the borrowing limit until days before the Treasury-imposed deadline, causing mild anxiety in financial markets but not forcing any broad sell-off.

Nancy Vanden Houten, a senior analyst at Stone & McCarthy Research Associates, has estimated that Treasury could probably make payments until March 14, but department officials worry that even if they can make most payments, a failure to raise the debt ceiling by their self-imposed deadline would cause intense concern in the markets.

Zachary Goldfarb contributed to this report.