Rep. Kevin McCarthy (R-Calif.) pushes back on criticism that he isn't conservative enough to be the new House majority whip. (The Associated Press)

House Republicans on Thursday overwhelmingly elected Rep. Kevin McCarthy to be majority leader and Rep. Steve Scalise to be majority whip, elevating a pair of lawmakers who promised a more open and conservative approach to running the chamber.

But the new team will quickly have to confront some of the old challenges of trying to hold together a fractious GOP caucus going into the final stretch of legislation before the 2014 midterm elections.

McCarthy, a congenial Californian aligned with his party’s business-friendly establishment, said he hoped to make the House GOP more effective.

“I’ll make one promise: I will work every single day to make sure this conference has the courage to lead with the wisdom to listen,” he said. “And we’ll turn this country around.”

Scalise, a Louisianan who leads an increasingly populist caucus of conservatives, promised to hold the party true to its core principles.

Rep. Steve Scalise (R-La.) says he won a three-way race for majority whip because his coalition was united, and says his election is "a win for America." (The Associated Press)

“We’ve got solid, conservative solutions that are going to solve the problems facing our country,” he said. “We’ve reached out to the president to join us in solving those problems. But we’re going to continue to move forward in the House as a united team.”

[ READ: Scalise’s win brings drama on big day in House ]

House Speaker John A. Boehner (R-Ohio) now has a relatively green leadership team surrounding him, with several fiscal policy fights on the horizon that could again divide the GOP caucus as it has been time and again since it reclaimed the majority in 2010.

With less than 40 days on the legislative calendar before November, the House has a small list of must-pass bills but one that provides several potential pitfalls: Funding for highway programs is drying up, the Export-Import Bank will lose the authority to provide key loans for U.S. companies competing overseas, and a stopgap federal budget must be approved to avoid another government shutdown.

Hard-line conservatives have vowed to make Boehner’s job difficult, opening up the possibility that he will need a deal with Democrats to win approval for each of those measures. How these matters are handled will help determine whether the new GOP leaders will face challenges for their jobs in the regular caucus elections after the November midterms.

Unlike departing House Majority Leader Eric Cantor (R-Va.), whose rise began a dozen years ago, McCarthy and Scalise have no connection to the previous generation of party bosses whose images have been shredded by today’s austerity-focused conservatives. McCarthy was first elected in 2006 and Scalise in 2008, one of the most junior combinations to hold those posts.

The first order of business, according to the new Republican leaders, was forging unity after a snap election Thursday that was prompted by Cantor’s loss in Virginia’s Republican primary last week. The leadership contests played out along the ideological fault lines that have bitterly divided the GOP on a national level over the past four years, as well as inside the House Republican Conference.

There's a House leadership shakeup after Majority Leader Rep. Eric Cantor, R-Va., lost his primary -- and with it, his seat in Congress. That leaves the majority leader position open, plus questions about who will step in as the Republican whip. But what do a majority leader and whip do, anyway? The Fix's Chris Cillizza has all you need to know. (Julie Percha/The Washington Post)

McCarthy clinched the race during a closed-door election, beating his lone competitor, Rep. Raúl Labrador (Idaho), who found it difficult to get votes beyond a small group of conservatives who helped him mount a failed coup against Boehner last year.

Scalise defeated the chief deputy whip, Rep. Peter Roskam (Ill.), and conservative Rep. Marlin A. Stutzman (Ind.) — and prevailed on the first ballot, a bold demonstration of how quickly he consolidated support in just nine days.

He rallied members of the Republican Study Committee, many of whom are Southern conservatives whose numbers have swelled in recent tea-party-fueled elections. With the Deep South shut out of key leadership posts and top committee chairmanships, Scalise based his candidacy on restoring that regional imbalance, given the bulging size of the Southern Republican bloc in the House. He distributed “Geaux Scalise” T-shirts and stickers that reminded colleagues of his native ties, but afterward he spoke of how he tried to appeal to all corners of the party.

“We built a strong team that was representative of our entire conference,” he told reporters.

Scalise’s role in leadership will be to serve as a bridge to conservatives who have caused Boehner and McCarthy the most trouble over the past three years. Some of the most conservative Republicans do not trust Scalise’s credentials, and that prompted Stutzman’s late entry into the race at their behest, but he is generally well liked by wide cross section of the right wing.

However, he will have to become a team player who votes for the sort of compromises he would have opposed in the past.

McCarthy, whose previous job required constant attention to the 233-member Republican caucus, now must provide a broader, more strategic role in shaping policy decisions. It’s a different job after a long stretch in which his political skills — a near encyclopedic knowledge of lawmakers’ family and political needs — played a key role.

Boehner was part of the 1994 leadership team that came into power without any blueprint for how to succeed, trying to take over the House after 40 years in the minority. One of his former leaders suggested Thursday that the internal politics would take care of itself if Boehner keeps the policy agenda flowing.

“We put aside political goals and focused on policy goals,” said Richard K. Armey (Tex.), a former House majority leader. “Speaker Boehner was part of all that. In my opinion, he needs to take command and run the House for the good of the American people. The politics will then take care of itself.”

Cantor will not officially leave his post until July 31, providing a long transition period for the new leaders. There also will be a five-week break in August and early September before the fall legislative agenda takes shape, and then an adjournment in October to allow lawmakers time to campaign before Election Day.

Some conservatives have suggested that they will muster a broad challenge to the top leaders in the fall, when they have more time to marshal their forces — or definitely by 2016.

“We’re evolving our leadership in a conservative direction,” said Rep. John Fleming (La.), who suggested that McCarthy “is good for another two years” but that he eventually will be replaced “with more and more conservative-leaning members.”

Others said that that was the wrong approach and that incumbency would be a boon for McCarthy. “The best chance for a change in leadership was today,” said Rep. Justin Amash (Mich.), who supported Labrador.

There was disappointment beyond the Capitol as well.

“The bad news is that the two winning candidates, McCarthy and Scalise, are business-as-usual, go-along-to-get-along Washington insiders,” said Richard Viguerie, a longtime conservative activist. “The gap between the leadership of the Republican Party and the base of the party continues to widen.”

Jackie Kucinich and Robert Costa contributed to this report.