Story highlights

House Speaker John Boehner on Wednesday brushed off the attempt to oust him

Rep. Mark Meadows, R-North Carolina, submitted a resolution on Tuesday to replace Boehner

Washington CNN  — 

House Speaker John Boehner on Wednesday brushed off the effort by one House conservative to oust him as “no big deal.”

“This is one member. I’ve got broad support amongst my colleagues,” Boehner insisted at his weekly press conference.

Blindsiding fellow Republicans and House GOP leaders, conservative Rep. Mark Meadows, R-North Carolina, launched an effort on Tuesday to remove Boehner as speaker.

On Wednesday, Boehner downplayed the idea of a revolt by the right, evidenced by the resolution that would strip him of his speakership and Texas Republican Sen. Ted Cruz’s criticism of Senate Majority Leader Mitch McConnell earlier this week.

“You’ve got a member here and a member there who are off the reservation – no big deal,” Boehner said.

He said he hasn’t spoken with Meadows since he launched the effort to remove him.

After repeated questions about the internal party fight, Boehner cut his last session with reporters in the Capitol before a long summer break short.

“I’m looking forward to a very successful fall,” he said.

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Meadows, who was among the group of House Republicans who voted against re-electing Boehner in January, filed a resolution to strip Boehner of his post as House speaker on Tuesday. It doesn’t specify who would replace him.

The two-page resolution ticks off a litany of complaints against Boehner, including “the speaker of the House of Representatives for the 114th Congress has endeavored to consolidate power and centralize decision-making, bypassing the majority of the 435 members of Congress and the people they represent.”

Boehner made it clear he didn’t think the resolution deserved a vote on the House floor. But several of his allies pushed for the leaders to bring up the resolution for a vote on Wednesday to prove that it didn’t have support to pass.

“I think it would be a good idea, personally, to put this behind us,” Arkansas Rep. Steve Womack told CNN.

Georgia Rep. Lynn Westmoreland also backed voting on the issue before the scheduled summer recess, but said the issue is “very divisive” and a lot of members didn’t want to take the vote.

Like many other House Republicans, Westmoreland was annoyed that the focus on the effort to remove Boehner was overshadowing the preferred summer message.

“Right now, we were going into the recess with a message that this was a bad Iranian deal, that Planned Parenthood is selling fetal baby body parts and that Hillary Clinton has got a two-month gap in her email between April and July of 2012,” Westmoreland said. “Those are the things we need to be talking about.”

Meadows faced his own blowback on Wednesday.

Fellow members of the House Freedom Caucus, a group he founded with other conservatives to push leaders to adopt their agenda, tried to kick him out of the group on Wednesday, according to two House GOP sources familiar with the discussion. There wasn’t enough consensus among the members to force him out entirely, but members discussed forcing him to resign from the board.

For now, Meadows’ spokeswoman said he is collecting signatures from fellow Republicans to force a vote on his resolution. But he would need to get a majority of House members – 218 – to sign up, a task multiple GOP members said he can’t pull off.

Some members expressed disappointment that there wasn’t more of an immediate consequence for Meadows for reigniting the storyline about the internal party squabbles between the speaker and conservatives.

“There’s a lot of things a speaker can do, but if you’re going to ask me what THIS speaker is willing to do, and I know John Boehner well, and we know his leadership style is not punitive in nature,” Womack told CNN. “It’s not confrontational in nature.”

Others were baffled that the North Carolina Republican attempted to overthrow the speaker without any real plan or organization behind him.

“I’ve been doing this a long time and that was the stupidest thing I’ve ever seen,” Westmoreland said..

Tuesday marked Meadow’s 56th birthday and he said he ran the decision to challenge Boehner by “several friends” in the House and his wife and children.

“I don’t like being in the limelight. It is fearful whenever you do doing something like this,” he said.

CNN’s Ted Barrett contributed to this report