Senate Majority Leader Mitch McConnell’s repeated ill-fated efforts to break filibusters of legislation to reject or impose conditions on the Iran deal have had an unusual side effect.

House Republicans, sick of being blamed for the gridlock in Congress and tired of passing bills that never get to President Barack Obama’s desk, have begun to direct their ire onto an unusual target: the Kentucky Republican.

McConnell is coming under increased pressure from members of his own party on the other side of the Rotunda to employ the “nuclear option” — that is, to change Senate precedents to allow certain measures to advance by a simple majority vote.

Current rules set a 60-vote threshold for any bill to clear a cloture motion. However, because Republicans only hold 54 seats in the Senate, any time there’s substantial Democratic opposition to a bill, it results in a filibuster. And Minority Leader Harry Reid, D-Nev., has proven adept at keeping his caucus together and keeping most bills from facing Obama’s veto pen.

Bringing the threshold down to 51 — as the nuclear option would achieve — would ensure Republicans’ priority bills get to move through the pipeline.

Frustration in the House Republican Conference reached a fever pitch over Senate Democrats’ filibuster of a disapproval resolution of the Iran nuclear deal, which prompted several House GOP lawmakers to call for lowering the vote threshold just for that single bill.

Over the past two weeks, demands for a more wholesale change have only grown.

At Wednesday night’s GOP presidential candidates’ debate in California, Wisconsin Gov. Scott Walker drew applause when he called for an end to the 60-vote threshold to push a bill defunding Planned Parenthood through the Senate.

“Forget about the 60-vote rule, there’s no reason — and the Constitution doesn’t call for 60 votes,” Walker said. “Pass it with 51 votes, put it on the desk of the president.”

And House Republicans, frustrated with the stalemate on the Iran agreement, increasingly say it’s time to bypass the Democrats.

On Thursday, Rep. Lamar Smith, R-Texas, and 56 fellow House Republicans sent a letter to McConnell and Reid urging the change.

“As Members of the House of Representatives, we respectfully urge the Senate to modify its rules to a majority vote threshold of 51 senators to approve some legislation. Some pieces of legislation, like the Iran nuclear deal, are simply so consequential that they demand revisions to the Senate’s procedures,” Smith and his colleagues wrote. “A move by the Senate to a majority vote that can approve some legislation would make it much easier for Congress to advance meaningful solutions to challenges our country faces.”

But House members have little sway on old-guard GOP senators, who, when asked about changing the rules, sometimes respond with a mix of derision and references to George Washington’s “cooling saucer” analogy.

House GOP leaders have also started to weigh in, a sign this may be more than a fringe effort from the rank and file.

On Wednesday night, House Republican Conference Vice Chairwoman Lynn Jenkins, R-Kan., released a statement calling for the end of the 60-vote threshold, the first member of leadership to take that public stand.

“Harry Reid opened the door to this last Congress,” Jenkins said of Reid, who, as majority leader, employed the nuclear option to break the GOP filibuster of Obama’s judicial nominees. “It’s time Senate Republicans walked through that door.

“Our nation cannot afford a government continually held hostage by Democrats unwilling to hold a vote on the critical issues facing America,” Jenkins continued. “These votes are simply too important to continue to be ignored.”

Another Kansas Republican, Sen. Jerry Moran, sounded a similar tone Tuesday on the Senate floor.

“The time has come to consider this issue of how the filibuster works. And it is because this issue is so important and the outcome of this debate so valuable to the future of our country and the security of the world that, in this case, we need to move forward with a majority vote to allow this agreement to be rejected,” Moran said.

At a House Republican leadership news conference on Thursday morning, House Majority Leader Kevin McCarthy, R-Calif., validated members’ frustration that they haven’t been able to see many of their big-ticket items go through the Senate.

“Yes, we are upset with who sits in that White House, but we have power in the House, we have power in the Senate, if the Senate would simply change a rule,” McCarthy said. “It’s not the Constitution. You ought to let their people have the voice.”

But some House Republicans, including leadership ally Tom Cole of Oklahoma, understand the Senate’s concerns.

“I’m thinking they’re being cautious and thinking we don’t want to be irrelevant with 48 or [49] members,” Cole told CQ Roll Call. “I think we’ve got a good chance to hold the majority, but I’m not going to be critical of McConnell or anybody else by saying we don’t, or if something really went wrong and you lost your majority in the House, wouldn’t you want us to be able to block a new Democratic president?”

From the sidelines of the news conference with McCarthy, Rep. Trent Franks, R-Ariz., vocalized his agreement, as if he was a parishioner at church moved by a sermon. “Yes,” he said with conviction.

The mounting cries for McConnell to “go nuclear” also come at a time when House Republicans are stuck on a strategy for funding the government while also defunding Planned Parenthood.

A contingent of conservative hardliners want to send the Senate a continuing resolution that includes defunding language as a policy rider. When Rep. Matt Salmon was recently challenged about that strategy — that it would not withstand a veto in the White House, let alone a Senate filibuster — the Arizona Republican’s answer was simple: Pull the trigger on the nuclear option.

“I think there needs to be a lot of added pressure … on Mitch McConnell to look at the nuclear option and expanding it from what Harry Reid did,” Salmon told reporters Thursday morning. “I mean, even McCain, who has been an ardent supporter of the modern filibuster rule, said last week maybe it was time to revisit that thing.”

Sen. John McCain, R-Ariz., did not respond too negatively when asked about the rules changes on a radio show last week but was more strident Thursday.

“The old line about the saucer,” McCain said. “There’s no doubt that [the framers] expected the Senate to be different. This would make us just like the House.”

“The problem with the nuclear option is we aren’t going to be in the majority forever,” McCain said.

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