Top progressive lawmakers Rep. Ro Khanna (D-Calif.) and Rep.-elect Alexandria Ocasio-Cortez (D-N.Y.) said this week they will vote against bylaws to govern the 116th Congress, a challenge to House Minority Leader Nancy Pelosi (D-Calif.), the likely next Speaker.

They are objecting to the inclusion of what's known as a pay-as-you-go budgetary rule, which requires that legislation be deficit neutral, meaning any costs would need to be offset with new revenue or cuts elsewhere.

But the two failed to convince other progressives in Congress to vote against the package, a good early sign for Pelosi, who will have to work to keep an ideologically fractured caucus together.

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Republicans such as outgoing speaker Paul Ryan Paul Davis RyanAt indoor rally, Pence says election runs through Wisconsin Juan Williams: Breaking down the debates Peterson faces fight of his career in deep-red Minnesota district MORE (R-Wis.) and his predecessor John Boehner John Andrew BoehnerLongtime House parliamentarian to step down Five things we learned from this year's primaries Bad blood between Pelosi, Meadows complicates coronavirus talks MORE (R-Ohio) faced constant challenges from the right flank of their party. That dynamic ultimately ended Boehner John Andrew BoehnerLongtime House parliamentarian to step down Five things we learned from this year's primaries Bad blood between Pelosi, Meadows complicates coronavirus talks MORE’s speakership, a fate Pelosi hopes to avoid.

House Democratic leaders adopted pay-go rules the last time they were in power, and Pelosi and incoming House Majority Leader Steny Hoyer Steny Hamilton HoyerDemocrats scramble on COVID-19 relief amid division, Trump surprise The Hill's Morning Report - Sponsored by The Air Line Pilots Association - Pence lauds Harris as 'experienced debater'; Trump, Biden diverge over debate prep Coons beats back progressive Senate primary challenger in Delaware MORE (D-Md.) indicated months ago that they planned to adopt pay-go rules again if Democrats won control of the House in the midterm elections.

Budget watchers say pay-go is an important budget tool for keeping the federal deficit in check, but Khanna and Ocasio-Cortez railed against it.

"It is terrible economics. The austerians were wrong about the Great Recession and Great Depression. At some point, politicians need to learn from mistakes and read economic history," Khanna tweeted on Wednesday.

Khanna said he's not whipping on the rules package but thinks that a few other members share his opinion. He said many members want pay-go to be eliminated from the rules package so that they are not put in a difficult position.

Ocasio-Cortez echoed previous criticism among progressives that the rule is "a dark political maneuver designed to hamstring progress on healthcare+other leg."

Pelosi spokesman Drew Hammill shot back, arguing pay-go would be an improvement from current GOP rules, which he called "CUTGO," that prohibit tax increases from being used to pay for legislation.

Without a pay-go rule in the House, he said, the White House budget office would be required by law to offset deficits from new legislation by cutting certain mandatory spending, such as Medicare.

"We must replace CUTGO to allow Democrats to designate appropriate offsets (including revenue increases). A vote AGAINST the Democratic Rules package is a vote to let Mick Mulvaney Mick MulvaneyMick Mulvaney to start hedge fund Fauci says positive White House task force reports don't always match what he hears on the ground Bottom line MORE make across the board cuts, unilaterally reversing Democratic initiatives and funding increases," he wrote, referencing the director of the White House Office of Management and Budget.

The pay-go rule would not block deficit-producing legislation from going forward, but it would create a legislative roadblock.

Eighteen Democrats would need to vote against the rules package on Jan. 3 to sink it. A failure to pass the rules package would be a significant setback for Pelosi on the same day she's expect to reclaim the Speaker's gavel.

But the gambit to block the rules did not catch on with the leaders of the Congressional Progressive Caucus (CPC). Co-chairs Rep. Pramila Jayapal (D-Wash.) and Rep. Mark Pocan (D-Wis.) said they would vote for the package despite concerns over Pay-go.

"Chairman McGovern and House Leadership have committed to us that PAYGO will not be an impediment to advancing key progressive priorities in the 116th Congress," Jayapal and Pocan said in a statement Wednesday, referring to incoming Rules Committee Chairman Jim McGovern (D-Mass.).

The two said they would advance legislation to change the statutory version of the rule.

The rules package was released after consultation with the CPC as well as with more centrist groups of House Democrats. Progressives got a win during the negotiations over the rules package when leadership agreed not to include a proposal to require a three-fifths supermajority for legislation that would raise taxes on lower-and middle-class families.

McGovern reiterated his commitment to preventing the rule from hampering progressive agenda items in his own tweet.

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“As a progressive and as Chairman of the Rules Committee, I’m going to do everything in my power to ensure it doesn’t prevent Medicare for All and other progressive causes from moving forward, including waiving the House rule,” he said.

Other members of the CPC followed the lead of Pocan and Jayapal, including outgoing chair, Rep. Raul Grijalva (D-Ariz.).

“I’m confident our leadership understands these issues and will work toward ensuring pay-go does not impede progress on the policy solutions Americans have demanded,” he said, indicating that he would vote for the rules package.

Khanna, the first vice chair of the CPC in the new Congress, told The Hill later on Wednesday that he is sticking to his decision to vote against the rules package, after Jayapal and Pocan said they would vote for it.

Khanna said a waiver to the pay-go rule may require a House vote.

"We should not give Republicans a talking point every time we ask for a waiver," he told The Hill. "We need to reject the entire frame of the austerity school of economics. We need to argue that our policies are pro-growth."

Rep. Tim Ryan Timothy (Tim) RyanLincoln Project hits Trump for criticizing Goodyear, 'an American company' Biden defends Goodyear after Trump urges boycott On The Money: Fed officials saw recovery slowing, virus threat growing | Trump urges boycott of Goodyear tires, prompts backlash | Analysis blames monopoly power for income inequality MORE (D-Ohio), who challenged Pelosi for the House Minority Leader position in 2016, hadn’t decided Wednesday evening how he would vote on the rules package but said that pay-go was a “no go” for him.

“We have too many investments to make to rebuild the middle class and make us globally competitive,” he said in a statement. “Critical investments in education, infrastructure, and health care should not be held hostage to budgetary constraints that Republicans have never respected anyhow.”

Sen. Bernie Sanders Bernie SandersSenate Republicans signal openness to working with Biden Hillicon Valley: DOJ indicts Chinese, Malaysian hackers accused of targeting over 100 organizations | GOP senators raise concerns over Oracle-TikTok deal | QAnon awareness jumps in new poll Schumer, Sanders call for Senate panel to address election security MORE (I-Vt.), the only Senate member of the Congressional Progressive Caucus, chimed in as well.

“At a time when climate change threatens our planet, when our infrastructure is crumbling, when 30 million people have no health insurance, I'm concerned that the concept of PAYGO will make it harder for Congress to address the many crises facing our working families,” he tweeted Wednesday, though he did not specify whether he was referring to the proposed House rule, an existing Senate rule, or the 2010 law that requires mandatory cuts.

Some budget experts said concern over the rule was overblown precisely because the House rules could be waived for high-profile bills.

"In a prior life, I spent plenty of time trying to make a House PAYGO rule have teeth and consequences," Zach Moller, who previously worked as a senior policy analyst at the Committee for a Responsible Federal Budget, wrote in response to Khanna. "This PAYGO rule, as proposed, is not that. Progressives should not lose a minute of sleep over it."

This post was updated at 7:15 p.m.