WASHINGTON – After the budget standoff ended in crushing defeat last week and the political damage reports began to pile up for Republicans, one longtime party leader after another stepped forward to chastise their less-seasoned, tea party-inspired colleagues who drove the losing strategy.

“Let’s face it: It was not a good maneuver,” Sen. Orrin Hatch of Utah, the senior Senate Republican and supporter of the deal that ended the showdown, said in an interview in the Capitol on Thursday. “And that’s when you’ve got to have the adults running the thing.”

At around the same time, roughly a thousand miles away in Mississippi, a 42-year-old Republican state senator, Chris McDaniel, was announcing his bid to take the seat of one of those “adults,” Sen. Thad Cochran, 75, a six-term incumbent and the picture of the Republican Old Guard whose vote to end the standoff McDaniel called “more of a surrender than a compromise.”

Insurgent conservative groups like the Senate Conservatives Fund, the Madison Project and Club for Growth immediately announced their support for McDaniel, chairman of the Mississippi state Senate’s Conservative Coalition and a former Christian-radio host, providing an early glimpse of what the next three years are likely to hold for the Republican Party.

The budget fight that led to the first government shutdown in 17 years did not just set off a round of recriminations among Republicans over who was to blame for the politically disastrous standoff. It also heralded a very public escalation of a far more consequential battle for control of the Republican Party, a confrontation between tea party conservatives and establishment Republicans that will play out in the coming congressional and presidential primaries in 2014 and 2016 but has been simmering since President George W. Bush’s administration, if not before.

In dozens of interviews, elected officials, strategists and donors from both wings of the party were unusually blunt in drawing the intraparty battle lines, suggesting that the time for an open feud over the Republican future has arrived.

“It’s civil war in the GOP,” declared Richard Viguerie, the veteran conservative warrior who helped invent the political direct mail business.

The moment draws comparisons to some of the biggest fights of recent Republican Party history – the 1976 clash between the insurgent faction of activists who supported Ronald Reagan for president that year and the moderate party leaders who stuck by President Gerald R. Ford, or the split between the conservative Goldwater and moderate Rockefeller factions in 1964.

Some optimistic Republicans note that both of those campaigns planted the seeds for the conservative movement’s greatest success: Reagan’s 1980 election and his two terms as president.

“The business community thought the supply-siders were nuts, and the country club Republicans thought the social conservatives scary,” said William Kristol, editor of the Weekly Standard, of those earlier squabbles. “That all worked out OK.”

Far from being chastened by the failure to achieve any of the concessions they had sought, the conservative grass-roots activists who helped drive the confrontation in Congress and helped fuel support for the 144 House Republicans who voted against ending it are now ratcheting up their effort to rid the party of the sort of timorous Republicans who, they said, doomed their effort to defund the health law from the start.

“This was an inflection point, because the gap between what people believe in their hearts and what they see in Washington is getting wider and wider,” said Jim DeMint, former South Carolina senator and current Heritage Foundation president, who, as a founder of the Senate Conservatives Fund, is helping lead the insurgency.

DeMint, a sort of political godfather to the junior Republican congressmen who engineered the health care fight and shutdown, said of his acolytes: “They represent the voices of a lot of Americans who really think it’s time to draw a line in the sand to stop this reckless spending and the growth of the federal government.”

But the party’s establishment leaders now have what they regard as proof the activist wing’s tactics don’t – and won’t – work.

“The 20 or 30 members of the House who have been driving this aren’t a majority, and too often the strategy – the tactic – was, ‘Let’s just lay down a marker and force people to be with us,’ ” said senior Republican strategist Karl Rove. “Successful movements inside parties are movements that persuade people,” he added. “The question is, can they persuade? And thus far the jury’s out.”

At its heart, this fight is the latest chapter of a long-running struggle for dominance between a generally pro-business, center-right bloc that seeks to tame but not exactly dismantle Washington, and populist conservatives who call for more extreme measures to shrink government.

Though the election and re-election of Obama may have radicalized many conservatives, the base’s fury has its roots in the two terms of his predecessor, Bush, whose expansion of Medicare, proposed immigration overhaul and 2008 bank bailout left many conservatives distraught.

“People just saw a party that had wandered away from its soul,” said Michael A. Needham, chief executive of Heritage Action.

But the conservatives’ sense of disillusionment with the establishment did not translate into success in the 2008 or 2012 nomination fights. And the divergent reactions to Mitt Romney’s defeat at the hands of Obama last year reignited a debate from after Obama’s defeat of Sen. John McCain in 2008.

Some establishment Republicans argued that the primary season helped drive Romney to take more conservative positions than he otherwise would have on issues like immigration. Grass-roots activists voting against him asserted that he lost because he did not truly embrace the conservative principles.

That argument has resurfaced this year in the Virginia governor’s race. The state’s attorney general, Ken Cuccinelli, a tea party enthusiast, is trailing Terry McAuliffe, a former Democratic National Committee chairman, in every published poll. And Republicans are already pointing to Cuccinelli’s strident views and the shutdown as the explanation for why the race may be out of reach.

Conservatives reject this line of thinking, arguing that Cuccinelli’s problem is he drifted from his roots and ran an overly safe campaign on the economy without responding to Democratic attacks on his social views.

The more important intraparty fight will begin playing out chiefly in Senate primaries next year, with the targeting of incumbents like Cochran; Mitch McConnell, the Republican leader; Lindsey Graham of South Carolina; and perhaps Lamar Alexander of Tennessee and Pat Roberts of Kansas.

Their perceived roles as moderating drags on tea party-inspired senators like Ted Cruz of Texas and Mike Lee of Utah in the shutdown negotiations have galvanized grass-roots organizations to elect more such Republicans.

DeMint said he thought the power of the establishment and its corporate money was waning. “It’s harder to buy influence in Washington now,” he said.

That is certainly true in the House, the bulwark of tea party conservatism thanks to the overwhelmingly Republican nature of many of the districts and the less-expensive campaigns necessary in them.

Regardless of what happens in next year’s midterms, the fight for control of the GOP will play most dramatically in the contest for the 2016 presidential nomination. If a candidate from the insurgent wing is to defy recent history and seize the nomination, he or she will have to run in a fashion that, organizationally, more closely resembles the sophisticated campaigns typically waged by establishment hopefuls.

What some Republicans hope is that they can find a candidate with the ability to bridge the chasm between the party’s two factions, somebody who is acceptable to the insurgents and will benefit from their energy but will also be able to win over swing voters.

“We want to elect a majority of senators and the president,” said Alexander, a former presidential candidate, secretary of education and governor. “And in order to do that we’ve got to persuade the American people that they can trust us with the government. And you don’t do that by shutting down the government and defaulting on the debt.”