The chairman of the Republican Study Committee says Sen. Mitch McConnell Addison (Mitch) Mitchell McConnellGraham: GOP will confirm Trump's Supreme Court nominee before the election Trump puts Supreme Court fight at center of Ohio rally The Memo: Dems face balancing act on SCOTUS fight MORE (R-Ky.) should step down as majority leader.

“I think he’s a huge part of the problem,” Rep. Mark Walker (R-N.C.) told NBC News, comparing McConnell to the manager of a losing baseball team.

He noted that usually when a team goes on a bad losing streak, it’s the manager, not the players, who is fired.

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“There’s a growing consensus that would be very happy if the fine senator from Kentucky called it a career,” Walker told NBC.

Walker leads a group of 150 conservative House GOP lawmakers.

House members have been increasingly frustrated with the Senate, which this week failed again to make progress on ObamaCare repeal.

A spokesman for McConnell declined to respond publicly to the criticism, but allies of the senator waived it off, noting that House members don’t vote in Senate leadership races.

No Republican senator has publicly expressed interest in challenging McConnell for the Senate’s top job, and even after the demise of the health-care repeal bill, Senate Republicans said his leadership position is safe.

House Democratic Leader Nancy Pelosi (Calif.) has also been under pressure to step aside, one McConnell ally noted, arguing that grumbling over leadership is nothing special on Capitol Hill.

McConnell’s longtime conservative critics are seizing on the health-care setback to put political pressure on the GOP leader, whom they have long viewed as a member of the Washington establishment.

McConnell suffered a blow this week when the candidate he backed in the Alabama Senate Republican primary, Sen. Luther Strange Luther Johnson StrangeSessions hits back at Trump days ahead of Alabama Senate runoff The biggest political upsets of the decade State 'certificate of need' laws need to go MORE, lost to former state Supreme Court Chief Justice Roy Moore, who vowed in a fundraising email to end McConnell’s reign as majority leader.

Speaker Paul Ryan Paul Davis RyanKenosha will be a good bellwether in 2020 At indoor rally, Pence says election runs through Wisconsin Juan Williams: Breaking down the debates MORE (R-Wis.), who works closely with McConnell, told CNBC’s “Squawk Box” on Thursday that frustration with the Senate is boiling over among House Republicans.

“We’re really frustrated. Look, we passed 373 bills here in the House — 270-some are still in the Senate,” Ryan told host Joe Kernen.

Ryan noted that the House has passed more bills at this stage of the Trump administration than at similar points in the Obama, Clinton and both Bush administrations.

Those accomplishments include legislation repealing and replacing the 2010 Dodd-Frank Wall Street Reform and Consumer Protection Act, border security legislation and education reform.

“We’re all frustrated in the House. The Senate has rules that perplex us, that frustrate us but it is the way our system works,” Ryan further lamented.

Other House Republicans, however, say senators like John McCain John Sidney McCainBiden's six best bets in 2016 Trump states Replacing Justice Ginsburg could depend on Arizona's next senator The Hill's Morning Report - Sponsored by Facebook - Washington on edge amid SCOTUS vacancy MORE (Ariz.) and Susan Collins Susan Margaret CollinsGraham: GOP will confirm Trump's Supreme Court nominee before the election Gardner signals support for taking up Supreme Court nominee this year Tumultuous court battle upends fight for Senate MORE (Maine) are bigger problems than McConnell.

Senate Republican Whip John Cornyn John CornynTumultuous court battle upends fight for Senate Texas Democrats roll out first wave of planned digital ads as Election Day nears Calls grow for Biden to expand election map in final sprint MORE (Texas), the second-ranking member of the GOP leadership and one of the most qualified candidates to serve as the next Senate Republican leader, on Wednesday said McConnell’s job is safe.

“Sen. McConnell’s standing as the leader in the Republican Conference I think is very solid,” he said.