With Boehner vanquished, conservatives turn their sights on Mitch McConnell
Senate Majority Leader Mitch McConnell talks to reporters after the Senate Republican weekly policy luncheon at the Capitol in Washington, July 8, 2015. REUTERS/Kevin Lamarque

Some of the U.S. Congress's staunchest conservative Republicans celebrated House Speaker John Boehner's resignation on Friday and trained their sights on a new target: Senate Majority Leader Mitch McConnell.

In a display of intense infighting of the sort that has consumed the party for months, Republican presidential candidate and Senator Ted Cruz of Texas told a crowd of applauding conservative activists at the Value Voters Summit in Washington:

"You want to know how much each of you terrify Washington? Yesterday, John Boehner was speaker of the House. Y'all come to town and somehow that changes. My only request is, can you come more often?"

When another Republican presidential hopeful, Senator Marco Rubio of Florida, interrupted his speech at the event to relay the news that Boehner was leaving, raucous cheers broke out.

Boehner announced he would step down in October after months of pressure from his party's right wing, setting up a battle over succession to the House of Representatives' top post and handing a victory to his most vocal critics.

One of them, Representative Mick Mulvaney of South Carolina, said the speaker's decision "should be an absolute warning sign to McConnell." He said the Senate leader should more assertively promote a conservative Republican agenda, including by changing Senate rules so that Democrats cannot easily block legislation.

Conservative Republicans have expressed frustration since the start of 2015, after Republicans gained eight seats and the Senate majority in the 2014 elections, about McConnell's seeming inability to lead the chamber in a more rightward direction.

“If anyone was doubtful as to whether or not there was a group of members who were really angry and frustrated and disappointed in how things were going, that was put to rest. ... This anger and frustration with how our party’s being run is real and now it’s very, very tangible," Mulvaney told reporters outside the House after Boehner said he was stepping down.

He said Boehner's departure had been necessary, adding, "You absolutely have to bring the Senate into the discussion. ... That focus now will invariably, and should turn to Mitch McConnell in the Senate."

A McConnell spokesman declined to comment for this story.

Representative Matt Salmon of Arizona said McConnell was the big stumbling block to a conservative agenda that Republicans had promised voters.

"Boehner has been tarnished by McConnell’s lack of leadership on numerous occasions," Salmon said.

For months, some House conservatives have urged McConnell to change the Senate's unique procedural rules so that legislation does not need a super-majority of 60 votes to advance. The Kentucky senator has shown no signs of pursuing this.

Meanwhile, conservatives have watched as bills such as a measure to defund President Barack Obama's executive actions on immigration have been stopped by the 60-vote requirement.

On Thursday, the Senate defeated Republican efforts to use a funding extension bill to cut off money to Planned Parenthood, clearing the way for a version without that provision that extends all previous funding through Dec. 11.

Salmon said Friday of McConnell, “He surrenders at the sight of battle every time.”

Asked why conservatives were taking aim at their own leaders, Salmon said, "The American people expect us to get the job done and there’s no person that is more important than getting the job done."