The Republican speaker of the House of Representatives, John Boehner, has a curious habit of pulling despairing faces when marching his divided troops into battle.

As he marched them back again on Wednesday, exhausted and bedraggled by their failed attempt to hold President Obama to ransom over his healthcare reforms, there is much of the same eye-rolling that characterised the start of their reluctant campaign. “We fought the good fight. We just didn’t win,” he told a radio interviewer.

But not all Republicans think they can shrug off the past two weeks just as easily.

Moderate senators Lindsey Graham and John McCain were this week practically begging Democrats to put them out of their misery. “We won't be the last political party to overplay our hand. It might happen one day on the Democratic side. And if it did, would Republicans, for the good of the country, kinda give a little,” pleaded Graham.

McCain, who opposed the risky House strategy from the outset, accused Democratic rivals of “piling on” in delight.

In the end, the terms of surrender could not have been more humiliating. Nothing remained of the Republican party's multiple demands for repeal of Obamacare, spending cuts, tax reform and environmental concessions. Instead, Boehner was left to rely on Democratic votes to end the shutdown and lift the threat of debt default by extending government borrowing authority.

Heritage Action, an influential conservative pressure group behind the Tea Party radicals, urged Republicans to focus on the 2016 presidential election. The Koch brothers, the biggest financial donors to Republicans, had cut and run last week, distancing themselves from the strategy of linking Obamacare to the budget. Senator Ted Cruz, who staged a 21-hour speech against Obamacare and only days earlier had been plotting with Tea Party congressmen in the basement of a nearby Mexican restaurant, slinked off insisting the fight would go on outside Congress.

For Cruz and the Koch-funded Tea Party groups, such defeats only strengthen their argument that it is Washington and mainstream Republicans who are dysfunctional, not them. Tim Huelskamp, a member of the Tea Party congressional caucus, summed up the mood of defiance. “I think the elites, the Washington establishment, have won the battle, but I think that we will eventually win the war,” he said after Boehner announced his retreat.

Asked if he meant the split in his party would separate “the wheat from the chaff”, Huelskamp smiled broadly, and said that was a phrase he often used on his farm, in Kansas. “People back at home realise not all Republicans are conservatives. And some Republicans are anti-conservative.”

But many mainstream Republicans fear their Congressional party has been dealt a mortal blow by the saga. Adam Kinzinger, a congressman from Illinois, summarised the growing frustration many Republicans feel toward their Tea Party colleagues over the damage caused by the shutdown and debt limit fight to the GOP in the polls.

“There are some people in my party that you cannot convince that this isn’t, somehow, beneficial,” he said. “I think anyone who looks at this and thinks shutting down the government is a great GOP strategy is probably at the forefront of ensuring we are not a governing party.”

Political strategist Chris Henick, a former adviser to George W Bush and Rudy Giuliani, predicts the party mainstream will also now look outside Washington to regroup, focusing on moderate Republican governors such as Chris Christie and the fiscal conservatism of younger congressmen like Paul Ryan to find new common ground.

“If there is a longer term strategy, at least into the second quarter of 2014, it will be focusing on Ryan and his growth strategy and taking a lead from the governors,” he said.

But many of the elements that used to bind Republicans together are in doubt, split further by social issues such as immigration reform and gay marriage.

“Mitt Romney used to talk of the Republican party as a three-legged stool based on foreign policy, fiscal policy and social policy, but in foreign policy there is fatigue after Iraq and everyone wants to play down the divisions over social policy,” added Henick. “Of all things the most consistent of the three has always been fiscal and economic policy, but this is where this battle has been fought – it's banged up a little bit, but at least it hasn't been sawn off.”

Some degree of internal bickering is normal between elections but if Republicans cannot succeed in sticking the economic leg back together, a more lasting split is not inconceivable, say those close to the party.

“As a national party we are going to be all over the map until we have a nominee that can pull various wings together and we won't see that emerge at least until the end of 2015,” added Henick. “It will be fractious; thinking we are going to be completely unified in the 2014 midterms is mistaken.”

Until then many will be revisiting history books and looking back 100 years to when Theodore Roosevelt split from conservative Republicans to form a breakaway group called the Progressive Party, saying he felt like “bull moose” on the run. “This could be somewhat like 1912 and the traditional wing of the Republicans could very well be the Bull Moose group of today with the Tea Party claiming to be the new mainstream,” warned Henick.