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House Speaker John Boehner on Wednesday downplayed an insurgent Republican's surprise bid to oust him, calling it "no big deal."

The speaker said the effort by Rep. Mark Meadows of North Carolina to strip him of his post "isn't even deserving of a vote," adding, "You've got a member here and a member there who are off the reservation."

Boehner responded at a news conference, a day after Meadows made his largely symbolic -- but nevertheless unprecedented -- challenge, filing a formal proposal that if approved would force a new election by the entire House to pick a speaker.

The proposal was referred to a committee stacked with Boehner's loyalists, and is unlikely to emerge. House GOP leadership sources told Fox News that the resolution is expected to sit before the committee for now, with no immediate plans to consider it.

Meadows' resolution, though, put the acrimony within the Republican Party on public display once again.

Further, it disrupts GOP leaders' plans of using the August recess to focus on the Iran nuclear deal and a web of other issues. Now, the House goes into recess with this debate churning, even if the push stands little chance of succeeding.

"We will be getting bogged down on who is speaker over the August recess," said Rep. Pete King, R-N.Y. "We could end up like a European parliament. We should be talking about Iran. It's terrible."

Meadows, who was disciplined earlier this year by House leadership, said in his legislative proposal that Boehner "has endeavored to consolidate power and centralize decision-making, bypassing the majority of the 435 Members of Congress and the people they represent."

Meadows told reporters on Tuesday that he hoped his action prompted a "discussion" with Boehner and other House leaders "about representing the American people. It's about fairness."

Meadows said he wants Boehner and other GOP leaders to make sure that "every voice and every vote is respected, and votes of conscience are respected and not punished."

Democrats seized on the unrest.

"As the American people look to Congress for solutions to the challenges they face, they increasingly see a Republican Congress dominated by obstruction, distraction and dysfunction," Drew Hammill, a spokesman for House Democratic leader Nancy Pelosi, said on Wednesday. He added, "The American people deserve better."

Last month, the leadership briefly stripped Meadows of his subcommittee chairmanship over his votes in a move supported by Boehner, but later relented after conservatives objected.

Fox News' Chad Pergram and The Associated Press contributed to this report.