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(CNN) —  

Kevin McCarthy announced Monday that he will run for Speaker of the House, in a bid to succeed the retiring John Boehner.

“We have made real progress towards shrinking an overgrown federal government and reforming our broken entitlement system,” McCarthy, who is currently the House Majority Leader, wrote in an email to his colleagues. “But our work is far from done. We can’t ignore the differences that exist, but we can and must heal the divisions in our conference with work, time, and trust. That is why I have decided to run for Speaker of the House and graciously ask for your support.”

In a nod to the national mood favoring outsider candidates in the 2016 GOP presidential race, McCarthy added, “I am also sensitive to what is happening outside of the Beltway. I want us to be much closer to the people we represent, and I want them to once again feel like this is their government, they are in charge, and we are here to serve them.”

If McCarthy, 50, were to gain the Speaker’s gavel, it would be one of the fastest ascents to the top of the House in recent congressional history. Just over two years ago, he was the Majority Whip, the No. 3 position in the House. He moved up to Majority Leader in August 2014 after Eric Cantor left Congress following a defeat in a primary election.

But some House conservatives have a message for McCarthy: Not so fast.

“We spend 16 months or more figuring out who should be the nominee of our party for president, I think … we need to spend more than a week to figure out who the candidates for Speaker are,” Rep. Mark Meadows, R-North Carolina, told CNN.

READ: Inside the battle for the next House speaker

Meadows, who tried to oust Boehner this summer, is a member of the House Freedom Caucus, a group of close to 40 conservatives who have been pressing leaders for bolder action on a series of issues. This group wants more time to develop a plan for how the House GOP would operate going forward before holding an election for a new slate of leaders.

“To just move everyone up and not change the process is to suggest the issue was John Boehner, and I don’t see the issue as John Boehner,” Meadows told CNN.

Meadows’ strategy to force a vote to remove Boehner failed in July, but it reignited deep internal divisions inside the House GOP – a dynamic Boehner cited Friday when he announced his resignation.

The Freedom Caucus, which is meeting Monday night, has not formally endorsed any candidate for Speaker or other posts yet, but its members will wield enormous influence. It’s unclear whether it will vote as a block, but its members want to extract some promises in return for their support. They are demanding the next leader be more willing to fight for conservative principles, present a long term vision, and allow the group to have a role in shaping the legislative agenda.

The North Carolina Republican isn’t ready to endorse anyone for Speaker or any other leadership positions, telling CNN he has traded calls with McCarthy, but hasn’t spoken directly to him yet.

Meadows acknowledged that McCarthy is clearly the front-runner to be the next Speaker, but maintained it’s not a done deal yet, saying, “there’s still a lot of uncommitted votes.”

READ: Why John Boehner quit

All House Republicans will huddle Tuesday evening for a special conference meeting to discuss what comes next in a post-Boehner House, but no date has been set yet for the leadership election.

Illinois GOP Rep. Peter Roskam, a former member of leadership, pushed for the session as a way to slow down the process. He hasn’t announced he’s running for any leadership job yet, but many believe Roskam is positioning for a seat at the leadership table, possibly as majority leader.

McCarthy’s backers say he’s already got strong support. He needs a majority of the 247 House Republicans to be elected by the House GOP conference. That vote is done by secret ballot behind closed doors.

But the new Speaker of the House isn’t officially installed until a majority of the full House of Representatives backs the party’s nominee in a vote on the floor with CSPAN cameras covering, which means getting 218 votes. If McCarthy fails to get commitments from the vast majority of conservatives, it’s possible a small group could derail his candidacy and deal him a very public embarrassment.

“I would be hopeful that any nominee put on the House floor would already have that 218 vote support in the conference,” Meadows said on Monday.

CNN’s Manu Raju contributed to this story.