House Speaker John Boehner arrives to speak to media on Capitol Hill in Washington on Wednesday.AP Photo/Carolyn Kaster

Speaker John Boehner is slated to retire Friday, setting up a busy legislative week as he tries to “clean the barn,” as he put it, for his likely successor, Rep. Paul Ryan.

The House will likely vote to authorize the Export-Import Bank and raise the debt ceiling before Wednesday’s internal conference election, setting up a Thursday floor vote to hand Ryan the speakership. That will leave it to the Senate to take up the debt ceiling measure after it finishes work on cybersecurity legislation on Tuesday. Senate leadership has said they will not vote on the Export-Import Bank reauthorization as a standalone bill.

Yet heading into Monday, House Republican leaders still do not have a concrete plan about how to raise the debt limit by the Nov. 3 deadline. A plan to do so with some conditions fizzled amid lackluster support last Thursday, and GOP members are increasingly resigned to another vote on a clean debt-limit increase as early as Tuesday.

Boehner’s allies have said his office has continued to speak with the White House about a spending deal as he heads for the exits, but Democrats have downplayed the possibility of a broad agreement, and President Obama has continually said he will not negotiate over the debt limit. GOP leaders are cognizant, meanwhile, that if they do not vote this week, they would be letting the issue drag on into the first week of Ryan’s speakership.

“The speaker is going to try to get that out of the way before Paul takes over,” Rep. Tom Rooney said Friday. “I know he’s trying to do something with the president, but we’ve been down that road so many times before. It would be great if he could come up with some big deal that makes us all feel great about ourselves, but if past is precedent, we’re going to end up doing a clean debt-limit vote sometime in the next two weeks.”

McCarthy and other leaders have said they do not have the votes on their side of the aisle to pass a clean increase. But several members said privately that they doubt his words are more than posturing to try to bolster Boehner’s negotiating position. The fact is, a cadre of GOP leaders, committee chairs, and centrist members have voted for a clean increase in the past, and stand willing to join Democrats to do so again.

“I don’t like to have to do it. We should be doing something to get the debt down. But when we don’t have 218 votes on our side, it’s tough to hold a position,” Rep. Devin Nunes, who voted for a clean increase in 2014, said. “I can’t imagine we are going to have a debt-limit crisis.”

For their part, Democrats have shown no interest in a potential deal to pair the debt ceiling to another must-pass bill, such as the Highway Trust Fund or a mandatory spending bill. "I don’t have any interest in any coupling," House Minority Leader Nancy Pelosi said Friday. "This is a non-negotiable: the full faith and credit of the United States of America."

Pelosi's No. 2, Whip Steny Hoyer, added that Hill Democrats are backing the White House's demand that debt-limit negotiations come without preconditions. "The president's view, which I share, is that the debt limit is not something that should be negotiated," he said. That doesn't necessarily preclude the debt ceiling from "riding" on another bill, but Hoyer saw such a scenario as unlikely. "If there is a carrier which can pass—but you only have five days. ... Therefore, we think a carrier is unlikely to be a viable option at this point in time."

Ultimately, Hoyer said, he believes that enough Republicans will cave and join a near-unanimous cohort of Democrats to raise the debt ceiling. "It's inconceivable to me that there aren't 30-plus Republicans to vote to make sure their country is solvent," he said.

If the House fails to address the debt ceiling this week, Senate leaders are preparing for the possibility that they will have to take the first step to increase the nation’s borrowing limit. With a deadline of next Tuesday, Senate Republican leaders are already forecasting concerns about their ability to get legislation through the upper chamber in such a short period. Without total cooperation from all members, the Senate could take about a week to pass a debt-ceiling increase, Sen. John Thune said last week.

But given the difficulty of getting to 218 votes in the House, Senate leaders are still hopeful that the lower chamber will go first, sending over a blueprint that they can attempt to rush to Obama’s desk before the deadline. Senate Majority Leader Mitch McConnell vowed not long after taking over the Senate this year that his majority would not allow a default under his watch, but several members are demanding concessions in exchange for raising the debt limit that could hamper his ability to pass a bill quickly.

Sen. Ted Cruz has called for strict cuts in federal funding, but said last week that the U.S. should not default. Sen. Rand Paul, Cruz’s presidential rival, told Fox News on Friday that Congress should not increase the debt ceiling unless Republicans get “significant reforms” in federal spending in return.

Neither Cruz’s nor Paul’s objections would be sufficient to kill a debt-ceiling increase in the Senate, but any senator could hold up the process with just eight days to go before the U.S. defaults.

Alex Brown contributed to this article

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