A bipartisan group of lawmakers is drafting a package of rules reforms that they want to see in the next Congress – and some members are even considering withholding their support for the next Speaker unless the candidate agrees to the changes.

The Problem Solvers Caucus discussed the ambitious idea on Thursday at a luncheon hosted by the bipartisan advocacy group No Labels, which works closely with the congressional group and is spearheading the so-called “Speaker’s Project.”

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The effort is aimed at changing how the House conducts legislative business in order to make the process more bipartisan and inclusive. One way to force that change is by encouraging members to withhold their votes for the next Speaker until they pledge to make the House rules more open and transparent.

There is expected to be a slim majority in the House next year, no matter which party wins control in the fall. That means that even a small group of lawmakers could have major sway over the selection of the next Speaker if they band together to demand changes.

“This is a huge opportunity, given the nature of how small the majority is going to be,” said Rep. Tom Reed Thomas (Tom) W. ReedCentrist House group offers bipartisan COVID-19 relief deal House approves two child care bills aimed at pandemic Diabetes Caucus co-chairs say telehealth expansion to continue beyond pandemic MORE (R-N.Y.), co-chair of the Problem Solvers Caucus. “The bloc of 10 to 20 to 40 members that we’re putting together could be highly influential.”

Members of the Problem Solvers Caucus, which is co-chaired by Reed and Josh Gottheimer Joshua (Josh) GottheimerCentrist House group offers bipartisan COVID-19 relief deal Hillicon Valley: Lawmakers introduce resolution condemning QAnon | US Cyber Command leader vows to 'defend forward' in protecting nation from cyberattacks House Democrats request briefing on seizure of terrorist cryptocurrency assets MORE (D-N.J.), have not yet publicly committed to the pledge. But a number of them are pursuing the idea, and are pitching it not only to other colleagues but also congressional candidates who are running for House seats.

“I can’t predict how many members will sign on, but if we commit and vote for this as a Problem Solvers Caucus, we also have to do this in a public way where we are held accountable,” said Rep. Ami Bera Amerish (Ami) Babulal BeraThe Hill's Coronavirus Report: iBIO Chairman and CEO Thomas Isett says developing a safe vaccine is paramount; US surpasses 150,000 coronavirus deaths with roughy one death per minute Democrats fear US already lost COVID-19 battle Karen Bass's star rises after leading police reform push MORE (D-Calif.).

It’s an idea that could gain steam, especially as both lawmakers and the public grow increasingly frustrated with a gridlocked and polarized Congress.

Moderate lawmakers in both parties also believe their influence will grow in 2019 if there is a narrow majority, which would give lawmakers in the middle more power to drive the agenda as leaders come begging for their votes.

“The country is rightly frustrated with the gridlock and they want us to get things done, instead of allowing small groups to obstruct,” Gottheimer said. “I’m hopeful that in the next Congress ... that our bipartisan group really has an opportunity to work together.”

But any effort to loosen the Speaker’s grip on power is likely to face fierce resistance in both parties. Lawmakers acknowledged that they will face immense pressure to fall in line after the November elections as the parties gear up to elect their next leaders.

“The amount of pressure that is going to be brought on members is going to be huge,” Bera said.

The Problem Solvers Caucus is still finalizing the exact rules reforms that they want to see. Among the ideas being considered include allowing more open rules and amendments; ensuring conference committees have members from both parties; eliminating a tool that allows any member to force a vote to oust a sitting Speaker; requiring that a lawmaker receive a larger majority to win the Speaker’s gavel; and eliminating a practice of only bringing bills to the floor that have the majority of the GOP’s support.