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WASHINGTON (CNN) -

This isn't how House Speaker John Boehner wanted to start 2015.

He's presiding over a historic majority in the House while the Senate is controlled by Republicans for the first time in nearly a decade. But the Ohio Republican is still wrestling with a familiar problem that could threaten his agenda over the next two years: conservative unrest.

That dynamic will be on display Tuesday when a small -- but vocal -- group of Republicans plan to vote against giving Boehner a third term as Speaker.

"I think a lot of Republicans are looking for a new direction," Oklahoma GOP Rep. Jim Bridenstine, one of those saying he'll back another candidate, told CNN.

This group, which includes about a dozen lawmakers, is almost certain to fail. But even if they don't block Boehner from another term wielding the Speaker's gavel, their opposition is a fresh reminder of Boehner's struggles to control his rank-and-file just as he and incoming Senate Majority Leader Mitch McConnell try to prove that Republicans can govern heading into 2016.

And the drama is all playing out amid turmoil in the leadership ranks after revelations that House Majority Whip Steve Scalise once spoke to a white supremacist group, unfortunate news for a party that is trying to expand its reach to minorities ahead of the next presidential election.

Although he already got the nod to keep his post by the House Republican conference after the midterms in November, Boehner doesn't officially get the gavel again until a majority of members vote for him on the House floor on Tuesday. If 29 GOP members vote for someone else, they can force a potentially embarrassing second ballot -- with the scene playing out on live C-SPAN cameras.

The opposition movement isn't entirely unexpected. Two years ago, Boehner faced a similar, poorly organized effort when a dozen House Republicans backed other candidates or declined to vote for him.

Some Boehner opponents say their position isn't personal. They just don't like the way he ran the House.

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