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.

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