A bill to raise the debt ceiling cleared a significant hurdle on Wednesday afternoon, after Democratic lawmakers supported Republican Speaker of the House Kevin McCarthy and allowed the bipartisan deal to advance to a full vote.

In order to see off a rebellion from members from his own party, McCarthy was forced to rely on the votes of 52 Democrats who joined 189 Republicans to approve a rule governing the debate on the legislation. That paved the way for a vote in the House of Representatives on the bill on Wednesday night.

Earlier, McCarthy had predicted the debt ceiling bill would “overwhelmingly” pass the lower chamber of Congress, as he raced to secure backing for the bipartisan deal, which would avert a damaging US default.

“We’ll get it done overwhelmingly,” McCarthy said in an interview with Fox News on Wednesday morning. “To govern is not easy. But I don’t want to be on the wrong side of history.”

The Speaker’s prediction came after he pitched the deal in an hours-long closed-door meeting with House Republicans on Capitol Hill on Tuesday night.

McCarthy announced at the weekend that he had struck an agreement with Joe Biden’s White House to suspend the debt ceiling until after next year’s presidential election. The deal caps federal spending for the next two years, speeds up the permitting process for big energy projects, cuts funding for the Internal Revenue Service and introduces new requirements for food stamps and other social safety net programmes.

The deal needs to pass both chambers of Congress if it is to be signed into law before the Treasury runs out of money. Treasury secretary Janet Yellen has warned the government would run out of money and be unable to pay its obligations on June 5 if the debt ceiling is not raised.

“We’re going to deal with the debt ceiling,” Biden said at the White House on Wednesday. “I think things are going as planned. God willing I’ll be landing in Colorado tonight in preparation for my commencement speech at the Air Force Academy tomorrow. And God willing by the time I land Congress will have acted, the House will have acted and we’ll be one step closer.”

McCarthy and the White House have been upbeat about the likelihood of the bill passing, even as critics in both parties have come out against the measure.

On the right, the hardline Freedom Caucus of House Republicans have attacked the deal for not imposing steeper spending cuts.

On the left, progressive Democrats, including Alexandria Ocasio-Cortez and Pramila Jayapal, have lambasted Biden for capitulating to Republican demands.

If the bill passes the House, it will head directly to the Senate. Mitch McConnell, the top Senate Republican, said on Wednesday that he expected the bill to pass the House, and would be “proud to support” the deal “without delay” when it is voted on in the upper chamber of Congress. After that, Biden would sign it into law.

Because Republicans control the House by a razor-thin margin, and more than two dozen Republicans have already said they would vote against the bill, McCarthy will be counting on the support of Democrats to get the bill over the line.

The Speaker’s whip count was bolstered earlier in the week when the leaders of the New Democrat Coalition, a group of nearly 100 centrist Democrats, said they were in favour of the agreement.

On Wednesday morning, the Problem Solvers Caucus, a group of 64 centrist lawmakers, equally divided between Democrats and Republicans, said they would also get behind the bill.

Hakeem Jeffries, the top Democrat in the House, said on Wednesday morning that he would support the bill “without hesitation, reservation or trepidation”, adding: “Not because it’s perfect. But in divided government, we, of course, cannot allow the perfect to be the enemy of the good.”

The bill faces opposition from lawmakers on both sides of the aisle in the Senate too. Bernie Sanders, the progressive senator, came out strongly against the deal on Wednesday, saying he could not “in good conscience” vote for the legislation because it imposes spending cuts without raising taxes on wealthy Americans.