The House of Representatives voted to advance a bill to raise the US debt ceiling, a major victory for Republican Speaker of the House Kevin McCarthy that brings Washington significantly closer to averting a damaging default.

The House voted 314-117 late on Wednesday to approve of the bill, after 165 Democrats sided with 149 Republicans and allowed McCarthy to see off a rebellion from some members of his own party.

In the end, 71 Republicans voted against the measure, many of them members of the hardline House Freedom Caucus.

The bill will now be sent to the Senate, which will also need to approve the measure in order for it to be signed into law by president Joe Biden and go into effect ahead of a looming June 5 deadline.

“I watch division in this House. But tonight, we might come together to do something very big for this country,” McCarthy said in a speech on the House floor ahead of the vote.

McCarthy announced at the weekend that he had struck an agreement with 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 new funding for the Internal Revenue Service and introduces new requirements for food stamps and other social safety net programmes.

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 by then.

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

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

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

The bill faces opposition from lawmakers on both sides of the aisle when it reaches the Senate too, although the House vote was always seen as a bigger risk to the legislation. 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.

Mitch McConnell, the top Senate Republican, on Wednesday said he would be “proud to support” the deal “without delay” when it is voted on in the upper chamber of Congress.

Chuck Schumer, the Democratic Senate majority leader, said he would bring the measure to the floor “as soon as possible” and urged colleagues to be “prepared to move on this bill quickly once it is the Senate’s turn to act”.

“I cannot stress enough that we have no margin, no margin, for error,” Schumer added. “Either we proceed quickly and send this bipartisan agreement to the president’s desk, or the federal government will default for the first time ever.”

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

Hakeem Jeffries, the top Democrat in the House, on Wednesday morning said 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.”