Speaker John Boehner on Friday told Republicans that, in order to avoid a default on the nation’s debt, lawmakers could face difficult votes on a deal as soon as Wednesday.

According to a GOP lawmaker, during a closed-door meeting Friday morning, the Ohio Republican indicated the hope is that a deal could be on the floor Wednesday, which would give the Senate five days to break any potential filibusters and pass the measure.

But the Republican lawmaker said that a Wednesday vote would likely require a final deal with “real numbers” in it and would need to be done by Monday because of continuing resentment within the Republican Conference over Boehner’s handling of the continuing resolution. The lawmaker said there is “lingering skepticism because of the CR” fight.

Following the meeting Friday, Boehner reiterated his insistence that he and President Barack Obama have not come to an agreement on raising the debt limit, saying there was “never an agreement, and frankly [we’re] not close to an agreement.”

According to Republicans in the meeting, Boehner continued to emphasize his support for the GOP’s Cut, Cap and Balance plan — which was defeated Friday in the Senate on a 51-46 vote and which never had a serious chance of becoming law.

Nevertheless, sources familiar with the negotiations said progress had been made and the two sides had returned to discussing what sorts of enforcement triggers could be used as part of a “grand bargain.”

Specifically, a source familiar with the negotiations confirmed to Roll Call that both sides are demanding triggers that would extract painful concessions from each party if a tax reform package is not adopted.

Obama’s proposed trigger would end the Bush tax cuts for people making more than $250,000 a year, while Boehner’s trigger would repeal the individual mandate in the health care reform overhaul.

Boehner refused to answer a question on the possibility of including the health care and tax provisions in the deal, saying simply, “There is no agreement. There is no deal in private. Our plan is Cut, Cap and Balance.”

But given the political realities on Capitol Hill, the prospect of passing what could amount to a tax increase for the nation’s wealthiest individuals was clearly making some Republicans uncomfortable.

“I don’t know if that’s the way to do it,” Rep. Bobby Schilling (R-Ill.) said following the Conference meeting.

At a Friday town hall at the University of Maryland, College Park, Obama seemed to acknowledge that the toughest road ahead might be in convincing House Republicans.

“We’re going to keep working on that. In 2010, Americans chose a divided government. They didn’t choose a dysfunctional government,” Obama said.

The president also said he knew his own party was upset with him about his proposed cuts to entitlements, insisting, “I wouldn’t make them if money wasn’t so tight.”

Boehner’s language in speaking about a deal — or lack thereof — is reminiscent of his statements during the waning days of the CR talks. Even as he was hammering out a deal in private with Obama, Boehner would repeatedly deny a deal existed, in public or private.

He also remained fully supportive of a House-passed measure that, like Cut, Cap and Balance, never had any realistic chance of being signed by Obama.

Steven T. Dennis and Christina Bellantoni contributed to this report.