Updated 4:37 p.m. | While conceding to a deadline of “before late February” to raise the debt ceiling, Speaker John A. Boehner, R-Ohio, said he still doesn’t have a plan for getting the votes from his conference.  

“I think we are still looking for the pieces to this puzzle,” Boehner told reporters at his weekly news conference Thursday. “But we do not want to default on our debt, and we’re not going to default on our debt.”  

Throughout the week, GOP leaders floated several bills they offered to tack on to a vote to lift the cap on the nation’s $17 trillion debt. In each case, they were rebuffed by the their rank and file, many of whom refuse to vote for a debt limit increase at all.  

“Mother Teresa is a saint now, but if the Congress wanted to make her a saint and attach that to the debt ceiling, we probably couldn’t get 218 votes,” Boehner told reporters.  

The House could act as soon as next week, GOP aides said, but the contours of a debt limit agreement remain in flux. Several aides and members conceded that the only option may be a debt limit increase without any added provisions.  

That is in large part because Democrats held firm on their demand for a clean bill, and Boehner probably can’t pass anything without their votes. White House Press Secretary Jay Carney said Thursday that President Barack Obama refuses to pay a “ransom,” but when asked whether something like the “No Budget, No Pay” provision from last year could be acceptable, Carney said exactly how the debt limit is raised would be determined by leaders in Congress.  

Minority Leader Nancy Pelosi was firmer in her stance.  

“Clean. Period,” the California Democrat said at a news conference. “This is not a matter of negotiation. … The only reason that the speaker is adding those things is because his caucus does not want to vote to honor the full faith and credit of the United States unless they have a cookie in their lunch. And that’s just not right.”  

Pelosi’s assertion notwithstanding, Republicans are hoping they can find a legislative sweetener to add to the debt ceiling increase that could attract at least some Democratic support.  

The latest option is a back-fill to cuts to military pensions slated to take effect in 2015 — part of the sweeping budget agreement both chambers approved earlier this year.  

Boehner and some of his top allies met over lunch Wednesday to discuss the plan and spoke with members during the evening’s vote series to round up support.  

Rep. Mike Simpson, R-Idaho, who was at the lunch with Boehner, said he thinks the idea could attract some Democratic votes, but said it remains unclear if it can pass.  

“I don’t know if they’d in unison say, ‘No,’” he said. “Right now they’re saying ‘No’ to anything. That’s the position that they’ve got, and what the president’s got. But can you find something that could get some of them? That’s the debate.”  

At the same vote series, leaders tested support for a temporary fix to a provision that helps the country control Medicare spending on physicians. That idea became less viable Thursday, when three major committees announced a deal on policy parameters for a long-term fix. The deal does not yet outline how to pay for the policy, however.  

Already off the table are two more ideas the GOP floated earlier in the week: Tying the debt limit increase to a measure kick-starting construction of the Keystone XL pipeline or a measure to repeal an arcane provision of the Affordable Care Act that helps insurance companies mitigate risk.  

Leaders’ next steps remain unclear, and will not likely be decided before they meet with their conference early next week. Treasury Secretary Jacob J. Lew said Congress has until the end of the month to pass a debt limit increase.  

Steven T. Dennis contributed to this report.