OKLAHOMA CITY — Oklahoma Republicans celebrated huge wins on election night, including the increase of GOP majorities in the state House and Senate to historic levels, but GOP leaders acknowledge the unprecedented growth will pose challenges for those who must now wrangle with a broader range of conservative ideology.

Republicans had a net gain of four seats in the Senate for a 36-12 advantage and three seats in the House for a new 72-29 margin — both the largest advantages ever for Republicans in the Legislature.

But the increasing majorities bring an infusion of new, far-right members of the Legislature who will stretch the conservative ideology and make it more challenging for House and Senate leaders and GOP Gov. Mary Fallin to reach a consensus within the chambers’ Republican caucuses.

“When you have that many members, herding the cats so to speak is a big job, and it takes someone with tremendous leadership abilities to pull it off,” Oklahoma Republican Party Chairman Matt Pinnell said. “But that doesn’t factor into my calculations. I want to win and win everywhere, and will continue to do that as long as I’m chairman.

“It’s that much more important to pick good leadership in the state House and Senate, and I think we have some of the best in (Senate President Pro Tem) Brian Bingman and (incoming House Speaker) T.W. Shannon.”

Bingman and Shannon both downplayed any notion of a growing rift within the party, but the challenges Shannon’s predecessor, outgoing House Speaker Kris Steele, faced within his own caucus were well-documented.

Steele was criticized by some of the more conservative House members at the start of his two years as speaker in 2010 when he suggested lawmakers should put the state’s struggling economy and budget hole at the top of their agenda over such issues as immigration, gun rights and abortion. Steele also failed to pull the caucus together at the end of the session for an agreement on a plan to cut the state’s income tax — a top priority of Fallin’s at the start of the session.

But Shannon, R-Lawton, was able to win a close election to become the next House speaker because of the support of the right wing of the caucus, and he continued to say Wednesday that he embraces the diversity of the Republicans in the House.

“I think it’s the most diverse caucus in the history of the state, and I think that’s a good thing,” Shannon said. “We’re going to have diverse opinions and healthy discussions and debate, and I think at the end of the day we’ll be able to work together.”

Fallin also welcomed the addition of new Republicans to the House and Senate and said her agenda of improving the state’s business climate, making government more efficient and reducing taxes won’t change.

“It’s all about bringing people together for a vision, building a consensus and moving an agenda forward,” Fallin said. “That’s what I’ll continue to do, no matter how many Republicans we have.”

But some House conservatives said they plan to keep pushing back against the current budgeting process and other policies endorsed by leadership, including the issuing of bonds to pay for infrastructure improvements.

“Bonding is constitutional, but it has to go to a vote of the people,” said Rep. Mike Ritze, a Broken Arrow Republican and self-described “constitutional conservative” who is among a growing number of Republican House members opposed to bond issues. “If we (allow) bonds without it going to a vote of the people, then I’m against it.”

Ritze and Rep. Mike Reynolds, an Oklahoma City Republican and frequent critic of leaders within his own party, have filed a lawsuit claiming a $2.5 million state appropriation for a youth livestock expo was unconstitutional.

“I have nothing against the youth expo,” Ritze said. “But you cannot use public funds for private use. That’s why we filed the lawsuit — to try and rein in some of the spending.”

Capitol observers like former Republican state Rep. Thad Balkman, now a lobbyist for the Oklahoma Lawyers’ Association, said it’s clear the growing pains of the Republican Party will provide a challenge to GOP leaders.

“There’s a struggle going on with Republicans who are used to being in the minority versus those who understand they’ve got to govern now,” Balkman said. “Therefore, governing implies that you do have to build coalitions, that you might have to compromise, and I think that’s not necessarily embraced by everyone in the Republican caucus in the House and Senate.

“I think as Republican majorities increase, you’re creating a larger tent inside the Republican Party, and I suspect that creates management issues for the Republican leadership, as we’ve seen in the House in previous years.”