House Speaker John Boehner (R-Ohio). (J. Scott Applewhite/AP)

Decisive midterm election victories in November put Republicans in a powerful position to move their own legislative agenda this year, but as the new Congress convenes Tuesday there are early signs of trouble in the House for the GOP’s expanded majority.

House Republicans are facing some of the same divisions that have hobbled their efforts to govern over the past four years, particularly on fiscal matters.

House Speaker John A. Boehner (R-Ohio) is again the central figure in a now-familiar drama as he faces a revolt from rank-and-file GOP conservatives who want to deprive him of a third term as speaker. While the mutiny seemed unlikely to succeed, it could inject some turmoil into the leadership vote Tuesday and is a reminder of the lingering discord that threatens to blunt Republican efforts to govern.

“We’re on probation, quite frankly,” said Rep. Phil Roe (R-Tenn.), who told reporters that Republicans must not overplay their post-election hand and become mired in intraparty squabbles. “We’ve got to perform for the next two years. . . . There is an expectation for us to do a lot of work, and I’m ready to get started.”

GOP leaders have said that their top priority is to put the disunity of the past four years behind them and demonstrate to the average American that they can govern without shutting down the government or watching the party rip itself apart. Some of the GOP’s top legislative goals — passing a budget the president will sign, replenishing the highway trust fund and overhauling the federal tax code — could present severe tests for Boehner, who has seen conservative anger derail his plans in the past.

While House Republicans’ 13-seat net midterm gain has put Boehner and his lieutenants in a stronger position to contain the rancor than in past years, there was a sense of deja vu over the Capitol on Monday, with at least 11 Republicans — current and soon-to-be members — lining up against Boehner. Two of them, Reps. Louie Gohmert (Tex.) and Ted Yoho (Fla.), offered themselves as replacements. Both voted against Boehner for speaker in 2013.

House GOP offices reported thousands of calls in relation to the speaker vote, with several of them reporting an average of 100 to 200 negative ones regarding Boehner on Monday alone.

Monday afternoon in the Rayburn House Office Building, a clutch of younger aides were spotted speaking nervously about Boehner’s chances; a few yards away, Gohmert’s office fielded ­media requests as its phones rang.

Boehner’s allies expressed confidence that he would retain his gavel and sent one another text messages Monday as news broke about the speaker’s latest defectors. Boehner spokesman Michael Steel said in an e-mail that the speaker expects to be reelected.

Rep. Tom Cole (R-Okla.), a Boehner supporter, said in an interview that “there are always malcontents.” He added: “If you go against your own colleagues by opposing the speaker on the floor, you will embarrass House Republicans and disrupt our team. It’d be unforgivable political behavior.”

Rep. Marlin A. Stutzman (R-Ind.) said Boehner’s opponents would dine together Monday night to go over their floor plan for Tuesday, mapping out who could possibly join them at the 11th hour.

“What I see is noise,” said former speaker Newt Gingrich (R-Ga.), who visited with Boehner on Monday and dismissed any suggestion that he is in danger of losing his job.

Democrats watching from the sidelines marveled at yet more leadership strife for Boehner, despite his larger majority.

“Our Republican colleagues are going to have a tough week as they start sweeping things under the rug,” said Rep. Ben Ray Luján (D-N.M.), the new chairman of the Democratic Congressional Campaign Committee.

As tensions mounted, Boehner opponents grew optimistic and felt the tide was turning in their direction, all while acknowledging the difficulties ahead. “There are a lot of members, more than a sufficient number, to pull this off,” said Rep. Thomas Massie (R-Ky.), who plans to vote against Boehner. “The only thing in our way is fear, fear by those who are worried about the repercussions of voting no. We’re doing everything we can to calm those fears.”

Massie, a libertarian, estimated that upwards of 40 Republicans are quietly open to opposing Boehner but would do so only if the leadership’s coalition began to crack on the floor.

But there was little evidence that the fringe contingent’s efforts would snowball into a widespread movement against Boehner. Neither Yoho nor Gohmert has broad sway in the House. Gohmert is a fixture on Fox News Channel but is not a major player in legislative matters. Yoho and most of the other possible challengers have a similar political standing: vocal, but backbenchers.

“What they’ve got is some grievances but no candidate,” said former congressman Bob Walker (R-Pa.), who added that the new majority is big enough to accommodate this latest bout of dissent. “You can afford to lose a lot more people when you have 246 seats than you can with a much smaller majority.”

Still, the flurry of opposition Monday came at an unfortunate time for Boehner. Rather than again managing the internal fights that have plagued the GOP since the 2010 tea party wave election, leaders had hoped to turn their attention to policy, striking a new tone ahead of the 2016 presidential election. Instead, they were dealing with a backlash against legislation they spearheaded in the previous Congress.

In statements announcing their opposition to Boehner, most of the speaker’s critics took issue with the $1.1 trillion spending bill that passed the House in December with the support of most Republicans and some Democrats, arguing it did not do enough to curb President Obama’s use of executive authority.

“I was really disappointed” by the spending bill, said Rep. Dave Brat (R-Va.). “We could have addressed immigration and we did not. We did provide the president with the funds he wanted. . . . I like Speaker Boehner. He’s a good man. But the problems demand new leadership.”

When the new Congress convenes Tuesday, 246 Republicans and 188 Democrats will be sworn into the House. A candidate for speaker must win a majority to clinch the job.

It wasn’t clear how many members would show up to the vote Tuesday, but Boehner probably cannot afford to lose more than about 28 Republicans.

Boehner made a series of personal calls Monday to ask his colleagues for their support. A Boehner aide said the speaker has been reaching out to members for weeks. But several Republicans said the calls began to intensify over the weekend as the speaker’s associates have become skittish. Both the aide and the members spoke on the condition of anonymity in order to discuss private conversations.

If Boehner does not have the necessary number of votes on the first round of balloting, a second round will be held.

Under that scenario, House Republicans would probably move to a closed-door session to figure out the party’s next step before returning for a second vote.

In 2013, Boehner was pushed toward that outcome when a dozen Republicans defected or did not vote, but he narrowly averted a second ballot.

House leadership aides have played down the grumblings of some of Boehner’s adversaries. But they privately acknowledged that the spotlight on Tuesday’s vote could create an unpredictable atmosphere, with the public glare and the television cameras potentially prompting some House Republicans to change their votes and join the anti-Boehner crowd.

At a regular meeting of conservative House Republican aides Monday, there was little to no discussion of efforts against Boehner, with more of the talk directed at the recent holidays and vacation adventures.

There were updates on events and on bills scheduled to come to the floor. Paul Teller, the chief of staff to Sen. Ted Cruz (R-Tex.), one of the chief agitators against Boehner in the past, was present, but the political intrigue was kept to a minimum, said several attendees who were not authorized to discuss the event.

The speaker vote is held by a voice roll call and can take more than an hour — a length of time that makes Boehner’s supporters uneasy. Boosters for the speaker will be throughout the chamber, ready to counsel on-the-fence Republicans, aides said.

Ed O’Keefe and Paul Kane contributed to this report.