(Bloomberg) -- The debt-limit deal struck by President Joe Biden and Speaker Kevin McCarthy is heading toward a vote Wednesday in the House of Representatives after clearing a crucial procedural hurdle with just days remaining to avoid a US default.

Legislation to suspend the US borrowing ceiling for a period and cap federal spending was advanced by the House Rules committee Tuesday night on a 7-6 margin, sending it to a vote on final passage by the full House.

House Majority Whip Tom Emmer, a Minnesota Republican, said early Wednesday that he’s confident the votes are in hand to move it through the chamber and send it to the Senate.

“Oh yeah, it’s going to pass today,” Emmer said on CNN.

Congress is racing to approve the measure before June 5, the date when Treasury Secretary Janet Yellen has warned the US risks default. Yet leaders in both parties face members who oppose concessions made by negotiators in the compromise unveiled over the weekend.

In one sign of growing momentum for the legislation in the House, the 64-member bipartisan Problem Solvers Caucus has agreed to back the legislation, an aide said early on Wednesday.

US Treasuries gained for a second day as traders assessed the likely impact of the debt-ceiling accord on future Fed policy decisions. The yield on the 10-year note dipped about two basis points to 3.66% as of 8:31 a.m. in New York, from 3.80% at the end of last week.

The bill would set the course for federal spending for the next two years and suspend the debt ceiling until Jan. 1, 2025 — postponing another clash over borrowing until after the presidential election. Biden and McCarthy have both said the measure would pass, and each spent much of the Memorial Day holiday lobbying members of their respective parties.

In exchange for Republican votes for the suspension, Democrats agreed to cap federal spending for the next two years. The White House interpretation of the caps has it telling lawmakers the deal would lower spending by about $1 trillion over a decade, while the GOP argues the spending cut is double that.

The nonpartisan Congressional Budget Office on Tuesday estimated that the bill would cut deficits by $1.5 trillion over 10 years.

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Bloomberg Economics economists Anna Wong and Maeva Cousin wrote on Tuesday that the two-year spending caps called for in the agreement “will deal an additional short-term blow to an economy already vulnerable to a recession. Yet they’ll barely dent the unsustainable medium-term trajectory of US federal debt — which we estimate is still on track to rise from 97% of GDP in 2022 to more than 130% of GDP by 2033.”

The bill’s fate was in question before Tuesday’s Rules Committee hearing, given the 13-member panel’s makeup, which includes several conservatives as well as four Democrats.

But Representative Thomas Massie of Kentucky, another conservative on the panel, voted to approve the measure providing enough votes to move it to the House floor.

“My purpose in being on this committee was not to imprint my ideology,” Massie said during Tuesday’s hearing. Massie later said he would support the bill. 

Representatives Chip Roy of Texas of and Ralph Norman of South Carolina, both members of the conservative House Freedom Caucus that has criticized the deal, voted against moving it forward, along with the panel’s four Democrats.

Leaders of both parties expressed optimism that the House would quickly pass the legislation. Wednesday passage in the House is critical to getting the bill through the Senate before the June 5 deadline. 

“We are going to make sure the country does not default,” House Democratic leader Hakeem Jeffries told Bloomberg Television’s “Balance of Power” on Tuesday. “We will be able to get this bill over the finish line tomorrow,” he said.

House Majority Leader Steve Scalise said after the Rules committee vote that “there were some members this morning who weren’t decided who had some very valid questions. And by tonight, they came up and spoke and said that they’re going to vote for the bill.”

Even so, dissatisfaction in conservative ranks escalated on Tuesday, with one Republican calling for McCarthy’s ouster.

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Representative Dan Bishop of North Carolina demanded a vote on his removal, claiming that the agreement granted too many concessions to Democrats. Roy promised a “reckoning” for McCarthy. Republican lawmakers, he said, had been “torn asunder” by the agreement.

Norman said “McCarthy has lost some trust.” 

Asked earlier Tuesday if he was worried about the possibility of being replaced as speaker, McCarthy responded: “Nope.” 

--With assistance from Paul Dobson, Emily Wilkins and Laura Litvan.

(Adds quote from Republican leader in third and fourth paragraphs and Problem Solvers Caucus support in sixth.)

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