Rep. Ro Khanna (D-Calif.) came out against the supermajority rule along with Rep.-elect Alexandria Ocasio-Cortez (D-N.Y.), not pictured. (Alyssa Schukar for The Washington Post)

House Democrats have backed off a proposed rule that would have made it more difficult for them to raise taxes and pass their most ambitious goals, an early victory for the left-flank of the party that is about to take control of the House.

Rep. Jim McGovern (D-Mass.), incoming chair of the House Rules Committee, told lawmakers Tuesday he will not advance “supermajority” rules requiring three-fifths majorities to approve tax hikes for most taxpayers, according to Rep. Mark Pocan (D-Wis.), co-chair of the Congressional Progressive Caucus.

An existing rule created by House Republicans requires a three-fifths supermajority vote in the House to approve any income tax increase. House Minority Leader Nancy Pelosi (D-Calif.) and other Democratic leaders proposed leaving the supermajority intact for most taxpayers, while scrapping the requirement for the wealthiest 20 percent of Americans and for corporations. But some liberal organizations and lawmakers said that did not go far enough, arguing that even the weaker rule would make it nearly impossible to enact progressive legislation such as Medicare-for-All or free universal college.

“We’re very glad to see that one go away,” said Pocan, who added the progressive caucus repeatedly expressed their disapproval of the proposal. “We ran in 2018 on increasing access to health care, and increasing people’s wages. ... Anything that took us off this conversation does not serve us well.”

The fight comes amid a broader battle in the Democratic Party over taxes, as an incoming crop of freshman lawmakers push the party to embrace social programs that require larger tax increases. Rep. Ro Khanna (D-Calif.) and Rep.-elect Alexandria Ocasio-Cortez (D-N.Y.) were the first two Democratic lawmakers to publicly express their opposition to the rule.

Democrats also face internal divisions over leadership’s support for the “pay as you go” rule (known as “PAYGO”), which would require new spending or tax cut legislation to be paid for without adding to the deficit.

Henry Connelly, a spokesman for Pelosi, said the rule was unnecessary to prevent Democrats from hiking taxes on the middle class. He also noted that House Republicans waived their rule to pass their tax law in 2017, because the legislation did raise taxes on some families.

“Unlike the House GOP, at the end of the day, the Democratic majority doesn’t need an arcane rule to keep our promise to protect middle class taxpayers,” Connelly said in an email.

But conservatives are likely to pounce on the move. Brian Riedl, senior fellow at the conservative-leaning Manhattan Institute, said Republicans may use the rule change to accuse Democrats of moving toward raising taxes on the American middle class.

“Republicans will likely use this to say Democrats are doing this to raise taxes, and it’s true,” Riedl said.

The richest fifth of taxpayers are those who make more than $108,000 annually, said Steve Wamhoff, director of federal tax policy at the Institute on Taxation and Economic Policy.