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 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 die-hards are swinging back hard, publicly 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 die-hards are angry.

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

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 when he seeks another term next month.

Republicans know that voters had delivered a strong message, one more difficult for party stalwarts to accept. 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 hardcore conservatives. He and his leadership team Monday offered a deficit reduction package that included $800 billion in new revenue; the die-hards oppose any new revenue. They booted the four Republicans off committees, and Boehner allies have been warning colleagues privately that more such punishment could be forthcoming.