A bipartisan group of centrist lawmakers is promising to withhold their votes for the next Speaker unless the candidate agrees to dramatically reform the House rules.

With 19 members of the bipartisan Problem Solvers Caucus signing the pledge, the group could have sway over the selection of the next Speaker — especially if there is a slim majority in the next Congress.

There are 10 Democrats and nine Republicans so far who are committed to the ambitious strategy, including some who are vulnerable this election cycle, such as Reps. Mike Coffman Michael (Mike) Howard CoffmanColorado mayor says he called protesters 'domestic terrorists' out of 'frustration' Colorado governor directs officials to reexamine death of Elijah McClain in police custody Petition demanding justice for Elijah McClain surpasses 2 million signatures MORE (R-Colo.), Leonard Lance Leonard LanceThomas Kean wins GOP primary to take on Rep. Tom Malinowski Gun debate to shape 2020 races GOP fears Trump backlash in suburbs MORE (R-N.J.), Brian Fitzpatrick Brian K. FitzpatrickHopes for DC, Puerto Rico statehood rise Florida Democrat introduces bill to recognize Puerto Rico statehood referendum DCCC reserves new ad buys in competitive districts, adds new members to 'Red to Blue' program MORE (R-Pa.) and Tom O’Halleran (D-Ariz.).

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Problem Solvers Caucus Co-Chairmen 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.) and Josh Gottheimer Joshua (Josh) GottheimerVulnerable Democrats tell Pelosi COVID-19 compromise 'essential' Centrist 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 MORE (D-N.J.) are hoping to get even more lawmakers from their 48-member caucus to sign the pledge, noting that they just picked up two more supporters in the last day.

“It’s 19 and growing,” Reed said at a press conference on Thursday. “And ... other members outside of the group are reaching out to us.”

Reed said they’ve discussed the concept with Blue Dog Democrats, moderate Republicans in the Tuesday Group and members of leadership from both parties.

“There are a lot of candidates we are speaking to on both sides,” added Gottheimer.

Leaders of the Problem Solvers Caucus have been working for months to get lawmakers on board with the effort, which they say is an attempt to “break the gridlock” in Washington.

The caucus, evenly split between Democrats and Republicans, unveiled a package of rule reforms this summer that are intended to make the House more bipartisan and inclusive. That step required agreement from 75 percent of the group and more than 50 percent of the caucus members of each party to formally back the proposal.

The proposal includes giving fast-track consideration to any bill with widespread support, making it easier to add amendments to legislation and making it harder for a small group of rebellious lawmakers to oust the House Speaker.

The package also would grant members a markup on one piece of legislation per session if it has a co-sponsor from the opposite party, as well as mandate a joint bipartisan meeting at the beginning of every Congress.

All of the ideas are designed to redistribute power, which reform advocates argue is too concentrated at the top, and empower more rank-and-file members in both parties.

“There’s too much power in too few hands,” Coffman said.

But for the proposal to actually have spine, the caucus is taking the next — and more difficult — step: asking lawmakers not to support the next Speaker unless the candidate agrees to overhaul the House rules.

The idea has picked up some steam, especially as lawmakers grow increasingly frustrated with the gridlock and polarization in Congress. In recent years, the far-right House Freedom Caucus has been highly successful at holding legislation on the House floor hostage by banding together as a unified voting bloc.

“We’re all frustrated. We want to govern again,” Gottheimer said.

Members of the Problem Solvers Caucus hope to sell their “break the gridlock” idea on the campaign trail this fall, where they think it will be a strong selling point.

“Of all the issues that concern residents in the district that I serve, the most important issue is not health care or taxation or immigration,” said Lance, who is in a tough reelection race. “The most important issue is bipartisan cooperation. ... And that is what we are attempting to do.”

The idea has some precedent for success: In 1923, a group of progressive Republicans demanded congressional reforms and withheld their votes for Speaker until the demands were heeded.

But any effort to loosen the Speaker’s — or majority’s — grip on power is likely to face fierce resistance from the old guard in both parties.