WASHINGTON - Republicans are in turmoil, split between die-hard conservatives and pragmatists in a battle for the soul and control of a party reeling from unexpected election setbacks last month.

The struggle is evident across the landscape. On Capitol Hill, Republicans are at odds over strategy and substance as they confront the fiscal cliff and a leader asserting his power over wayward members. Among voters, polls warn that Americans would blame Republicans if economic chaos ensues, while conservative interest groups insist this is no time to compromise. And among GOP insiders, a brawl could be looming over who chairs the party.

The schism is being aggravated almost daily in Congress, where the two factions are waging a fierce fight over how to deal with the budget crisis. House Speaker John A. Boehner (R., Ohio), a veteran pragmatist whose instincts for compromise had been thwarted by the rise of the die-hard conservatives, is his old self, offering deals and punishing those who defy him. The diehards are swinging back hard, questioning Boehner's leadership and offering reminders that they still have considerable financial and political muscle.

Republicans perceived as disloyal to Boehner are being punished. Four have been kicked off committees, and the diehards are angry.

"When one comes here and votes his conscience, and it's not antithetical to the Republican platform, why should he suffer for it?" asked Rep. Trent Franks of Arizona. "The Republican cause, and the cause of freedom, is diminished."

The rupture is a preview of things to come as the party begins charting a highly uncertain future.

Republicans were jolted on Election Day by losses. Not only did President Obama crush Republican Mitt Romney in the electoral vote count, but the party lost seats in the Senate and the House.

The party leadership is far from secure. Former Rep. J.C. Watts, once the House's highest-ranking black Republican, is being mentioned by some insiders as a possible challenger to Republican National Committee chairman Reince Priebus.

Obama and fellow Democrats won with a pledge to raise taxes on the wealthy, a position virtually all Republicans ruled out.

Pragmatists have been slowly moving in a more conciliatory direction. Day after day, it seems, a previously unshakable Republican suggests he could accept some higher rates. The latest was Sen. Tom Coburn of Oklahoma, long regarded as a no-tax-increase hard-liner.

At the same time, Boehner has defied the hard-core conservatives. He and his leadership team on Monday offered a deficit-reduction package that included $800 billion in new revenue; the diehards oppose any new revenue.

At the same time, conservative groups argue that unless Republicans stick to long-held fiscal principles, the party will stand for nothing - and, they warned, could face an uprising in 2014.

"You are entering a period of testing," said a letter to congressional Republicans signed by about 100 conservative leaders. "The whole leftist apparatus is gearing up to panic you and to force you to cave in. Don't do it."