Jacquelyn Martin / AP

Republicans in Congress have finally, at long last, found a speaker of the House. Now, they have less than two weeks to find a way to raise the debt ceiling.

The nation will exceed its borrowing limit by November 3, according to a series of increasingly urgent letters and public statements by Treasury Secretary Jacob Lew. And Speaker John Boehner has said he wants to deal with the debt ceiling before he leaves Congress on October 30, both to avert an unprecedented U.S. default and to dispense with an annual political headache before his successor is sworn in.

Yet as is so often the case with the debt limit, the task is proving more difficult than it seemed. Nearly five years into their House majority, most Republicans still cannot stomach the thought of voting to raise the debt limit without significant concessions, in large part because their constituents have been led to believe that they would be voting to authorize huge amounts of new spending, rather than paying for bills Congress has previously incurred. At the very least, GOP lawmakers believe the debt-limit hike should be used as an opportunity to impose fiscal discipline, but President Obama and congressional Democrats have held firm in their refusal to negotiate on what they say is a routine congressional responsibility.

The simplest way to handle it—as Democrats and moderate Republicans frequently point out—is for Boehner to bring up a clean bill extending the Treasury’s borrowing authority for at least another year. That’s what Boehner did the last time it came up, in February 2014, when he abandoned his previous demand that an increase in the debt ceiling be accompanied by equivalent cuts in spending. That measure passed narrowly, with just 28 Republicans joining all Democrats in support.

Boehner might not have his own political capital to worry about since he’s already quit, but his challenge now is numbers: Because Republicans expanded their majority last year, there are fewer Democrats in the House, and several more GOP lawmakers would need to vote yes for the bill to pass. “That’d be difficult,” Boehner told Bret Baier on Tuesday when asked about the prospects for a clean bill. “Our members want real reforms.” He said he’d been talking with Obama for the last month about a budget deal that would include an increase in the debt limit, but then accused the White House of walking away from the talks. “So we’re kind of left holding the bag, and we’re going to have to find a way forward,” Boehner said.

Cajoling another handful of Republicans shouldn’t be too difficult, and yet with the deadline 11 days away, he isn’t quite ready to bring up a clean debt bill. He’s been getting no help from the Republican-led Senate, which has thus far been waiting for the House to act on the issue. Instead, Boehner first returned to the familiar strategy of advancing a conservative proposal that would pair a debt-limit increase with significant cuts. The bill would face a certain veto if it ever made to Obama’s desk, and according to reports Thursday, it might not even come up for a vote in the House.

A Republican leadership aide said no decisions had been made about the debt limit, which in itself is a signal that Boehner’s next move might be to bring up a clean bill sometime next week. If recent history is a guide, congressional leaders schedule the toughest votes at the last minute, when lawmakers have no alternative to voting yes. As Treasury secretary, Lew is well aware of that dynamic, having been through this congressional high-wire act several times before.

The markets aren’t worried yet—the Dow soared more than 300 points on Thursday. Yet even Lew has admitted to wondering if this time is different, if paying the bills might be too much to ask of a Congress that can barely find someone to lead it. “I worry every time we hit this that sometime there would be an accident,” Lew said earlier this week. “And that would be terrible.”

We want to hear what you think about this article. Submit a letter to the editor or write to letters@theatlantic.com.