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.) said he and some other Republicans are committed to backing Nancy Pelosi Nancy PelosiHoyer: House should vote on COVID-19 aid — with or without a bipartisan deal Ruth Bader Ginsburg lies in repose at Supreme Court McCarthy threatens motion to oust Pelosi if she moves forward with impeachment MORE (D-Calif.) for Speaker if she agrees to enact a package of rule reforms.

Reed, co-chairman of the bipartisan Problem Solvers Caucus, said the growing frustration with gridlock, polarization and a top-heavy leadership approach in Congress are the reasons why several members in his party are willing to supply Pelosi with some Speaker votes in exchange for extracting an overhaul of the House rules.

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“I would be willing, as a Republican on the floor of the House, to support a Speaker candidate, including Nancy Pelosi, who supports these rule reforms,” Reed said at an event for The Hill sponsored by American University's School of Public Affairs and the Kennedy Political Union.

“There are other members that are as committed as I am to this on the Republican side that are willing to do that. But I’ll let them address it individually,” he added.

“That’s a big deal!” interjected Rep. 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.), Reed’s fellow co-chairman on the Problem Solvers Caucus.

Pelosi is fiercely working to line up as many votes as possible as she seeks to reclaim the Speaker’s gavel, with a vocal group of insurgents plotting to take her down. The group claims to have more than 20 lawmakers willing to vote against her on the House floor, which would be enough to block her accession.

But at a jam-packed press conference at the Capitol on Thursday, Pelosi said she has the votes, right now, to win the gavel on the floor with only Democratic support. And she said she would refuse any offers of help from the Republicans.

“Oh, please,” she said. “No, never.”

“I intend to win the Speakership with Democratic votes,” she said.

If some Republicans cross the aisle and back Pelosi for Speaker, they will have some cover from the White House. A day after Republicans' midterm drubbing, Trump endorsed Pelosi for Speaker and even suggested some Republicans should vote for her, though some have speculated that he just wants to have the GOP’s most well-known foil atop the Democratic caucus.

“In all fairness, Nancy Pelosi deserves to be chosen Speaker of the House by Democrats,” Trump tweeted last week. “If they give her a hard time, perhaps we will add some Republican votes. She has earned this great honor!”

Any Republican who votes for Pelosi on the House floor would be sure to face fierce criticism on the right and could open themselves up to a primary challenge. Reed acknowledged the tough situation, calling it “bizarro world.”

But Republicans could opt to just vote “present” on the floor, which could help give Pelosi the gavel by lowering the overall threshold she needs to clinch it.

Meanwhile, nine Democrats have vowed to withhold their support for Pelosi — or any other Speaker nominee — unless the candidate commits, in writing, to certain changes in House rules designed to empower rank-and-file lawmakers.

Pelosi huddled with Democrats from the Problem Solvers Caucus on Wednesday to discuss their proposed rules package, with Gottheimer saying Pelosi was receptive to the changes. Pelosi is now crafting her own proposal that will outline what she is willing to commit to, which she is expected to send to the caucus next week.

“Yesterday we had a very productive conversation. Went through each of the proposed rules, agreed on some, there were some ideas on how to make them better,” Gottheimer said. “And now, we’re waiting to see, in writing, the specifics in terms of what Leader Pelosi is willing to support in our caucus and on the House floor.”

The Problem Solvers rules package consists of 10 proposals designed to empower individual members and grease the skids for passage of popular bipartisan bills that, in recent years, have frequently been ignored.

Central to their reforms is a proposal requiring a supermajority vote — three-fifths of the House — to pass any legislation brought to the floor under a closed rule, and another ensuring fast-track consideration of any bill co-sponsored by at least two-thirds of the chamber.

It also proposes changes designed to prevent a small group of hard-liners from using threats to “vacate the chair” as a bludgeon to keep certain legislation off the floor, as the far-right Freedom Caucus has done in recent years.

In addition to working to win over Problem Solvers, Pelosi also appears to be targeting the Congressional Black Caucus, whom she met with Wednesday morning at the Democratic National Committee headquarters.

The next day, Pelosi’s office blasted out a statement touting her endorsement from Rep. Bobby Rush Bobby Lee RushCongress should investigate OAS actions in Bolivia Rep. Bobby Rush introduces legislation focused on addressing racism, lack of diversity in the federal government House Democrat introduces bill to replace Confederate monuments nationwide MORE (D-Ill.).

"Nancy Pelosi has my vote for Speaker," Bass wrote.

Mike Lillis contributed.