“I am staying on the Benghazi committee, period, exclamation point,” Rep. Trey Gowdy (R-S.C.) said in response to a campaign to draft him into the race for new House GOP majority leader. (Andrew Harrer/Bloomberg)

A generation of House Republicans who have spent the past five years trying to shake up Washington spent Tuesday trying to shake up their party’s leadership contests that have moved coolly toward reinforcing the status quo. They had little success.

A campaign to draft one prominent, relatively young conservative, Rep. Trey Gowdy (S.C.), into the race for majority leader was extinguished before day’s end, leaving restless conservatives to continue their search for a standard-bearer.

Meanwhile, the sitting majority leader, Kevin McCarthy (Calif.), moved to tighten his grip on the speaker’s chair being vacated next month by John A. Boehner (Ohio), pledging in a series of public appearances to “change the culture” of the Republican conference in a bid to address the right flank’s long-running frustrations with Boehner.

Both developments reflect an ongoing struggle among the newest members of the House GOP, elected in the tea party wave of 2010 and in subsequent years, to translate their zeal for conflict — with both President Obama and the Republican establishment — into a coherent vision for managing the fractious Republican majority and grooming leaders capable of executing such a vision.

The leadership jostling comes as the fiscal year comes to a close Wednesday without a new budget in place, requiring lawmakers to act to avoid a government shutdown beginning at 12:01 a.m. Thursday. Congress on Wednesday is expected to approve a stopgap spending bill that would keep the government open through Dec. 11.

House Republicans are facing a leadership reshuffle within their ranks — but as some lawmakers pull the party more toward the right, can any leader really restore unity? The Post's Robert Costa takes us inside the infighting in the Capitol. (Julie Percha/The Washington Post)

For House Republicans, the leadership grumblings are also a matter of style, with members of all generations saying they want to inject more swagger into a party that for months has been meekly navigating through infighting and chaos.

“Many members want the leadership to be more vocal across the board,” said Rep. Ted Poe (R-Tex.). “Things we bring up need to have more enthusiasm. Back home, they wouldn’t mind a little more fire and brimstone.”

Gowdy’s spin in the spotlight came amid doubts among some members about whether the two declared candidates to succeed McCarthy should he win the speakership — House Majority Whip Steve Scalise (La.) and Budget Committee Chairman Tom Price (Ga.) — possess the necessary backbone and messaging savvy.

Scalise is popular with members but is a low-key presence who prefers to build ties over long dinners of Creole food in his second-floor office suite. Price is a taciturn, well-respected conservative who has devoted his career to limiting government spending.

Coupling either with the mild-mannered McCarthy, to many House Republicans, would mean maintaining an upper echelon of leadership without a firebrand able to represent the agitations of the Republican base.

Gowdy, 51, is also a conservative Southerner, but one with the flair of the criminal prosecutor he once was. And, even more crucially, he is a product of the 2010 tea party movement that delivered the House majority to the GOP. His ascension to leadership would mark a generational milestone in a Republican caucus in which well over half the members have served three terms or fewer.

He also has built alliances across the House GOP’s internal divides. Boehner entrusted him with leading a select committee on the 2012 attack on U.S. facilities in Benghazi, Libya — a post that has made him a fixture on cable news and a hero to conservative activists.

That panel has been deeply involved in investigating Hillary Rodham Clinton’s use of a private e-mail server as secretary of state. The Democratic presidential candidate will testify before the select committee on Oct. 22, putting Gowdy at center stage.

A long-simmering campaign to draft Gowdy into a leadership post reemerged Tuesday morning during a Fox News Channel appearance by Rep. Jason Chaffetz ­(R-Utah), chairman of the House Oversight and Government Reform Committee. “If you want the best person to make the Republican case, if you want the best person to talk about why conservatism is the right answer for America, Trey Gowdy is our best foot forward,” Chaffetz said.

And Rep. Mia Love (R-Utah), a first-term member who has been embraced by conservative leaders, endorsed Gowdy: “With impressive communication skills, genuine compassion and the tenacity of a prosecutor, he will unite the party and the people around a truly American agenda.”

But Gowdy moved to tamp down the draft discussion and eventually squelched it entirely. “I am staying on the Benghazi committee, period, exclamation point,” he said before a Tuesday afternoon House vote.

That decision could partly reflect political reality: Scalise and Price have both been gathering support for days, seeking to contact each of the nearly 250 other Republicans who will pick the new leadership slate.

“Anybody can run, but this is probably a little late in the process,” Rep. Lynn A. Westmoreland (R-Ga.) said about Gowdy. “These guys [Price and Scalise] have been calling folks for a long, long time. There’s a lot of commitments already made.”

But the draft-Gowdy bid could be revived if the majority-leader contest, to be conducted by secret ballot at a date yet to be announced, takes an unexpected turn.

House Republicans met behind closed doors Tuesday evening in the Capitol basement in a special meeting called to discuss the path forward for the caucus. “By definition, John Boehner’s resignation says that there is a level of discontent that is unprecedented,” said Rep. Peter J. Roskam (R-Ill.), who proposed the meeting.

Style, he said, would be on the agenda: “We need leaders who are more aggressive in terms of communicating. . . . It seems like so many times the House is playing defense. What’s the plan to play offense?”

Inside, members discussed concerns, including minute procedural issues and deep-seated dismay with the House GOP’s drift. Gowdy, in emotional remarks, formally withdrew from a leadership race he never entered, explaining he needed to concentrate on the Benghazi probe, earning a standing ovation. Boehner did not attend.

“It was a therapy session,” said Rep. Carlos Curbelo (R-Fla.).

McCarthy, meanwhile, in his first public remarks since formally announcing his speaker run Monday, suggested that Boehner had lost touch with the Republican electorate and that he would lead a careful effort to reestablish trust among GOP voters.

Standing at Boehner’s side Tuesday morning, McCarthy seized on a “generational” shift and said he would be “closer to the people” when asked how he would differ as speaker.

“I know what’s going on across the country, and I’m concerned about what we hear,” he said. “A lot of people in Washington are concerned about power and institutions. I’m concerned about making a difference in everybody’s life. We want to make sure that we’re closer to the people, that they feel this is their government, they’re in charge, and we serve them.

Focusing on stylistic improvements rather than specific policy positions is a calibrated strategy to help McCarthy win support across ideological lines — particularly among the hard-core conservatives who led the drive to oust Boehner.

On “CBS This Morning” on Tuesday, McCarthy said those conservatives “very well could” challenge his leadership. “But a lot of them I’ve worked with; some of them are supporting me,” he said.

“A lot of people think being speaker is like a team manager,” he added. “I view it as a team captain. I’m a part of the team. Let everybody engage. Make it bottom up. And the more people engage, the more committee works, the more you will get a better outcome and a solution.”

Monday night on Fox News Channel, McCarthy indicated he would be more combative than Boehner: “We need to fight, but we need to fight to win.”

Paul Kane and David Weigel contributed to this report.