WASHINGTON (AFP) - Weakened and divided after a bruising budget standoff and two-week government shutdown, Republicans bickered on Sunday over who to blame for the resulting damage to their party brand.

The party suffered a major hit in the polls after the crisis, with more Americans blaming Republicans than Democrats or President Barack Obama for the shutdown.

Asked about the lasting impact on Republicans, a dour Senator Lindsey Graham told CBS television that it is a time of "soul-searching" within his party.

"It's a wake-up call," Mr Graham told CBS television's Face The Nation programme, adding that his party's self-inflicted woes have played into the hands of Mr Obama and congressional Democrats.

"I think we've learned this was a political gift to the president by the Republican party at a time he needed it the most," said Mr Graham, a longtime party elder.

"As a party we have to do soul-searching," Mr Graham said.

Republican leaders acknowledged on Sunday that they were still assessing how to recover from the debacle that saw the party acquiesce to Mr Obama and his allies, with little to show for it.

The standoff was precipitated in large part by Republican opposition to the president's signature health reform programme, dubbed Obamacare by its opponents, that went forward even in the midst of the shutdown, although the rollout has generally been viewed as somewhat rocky.

Top Senate Republican Mitch McConnell on Sunday decried burn-the-house-down tactics employed by the Tea Party, which spearheaded a shutdown he said has proved antithetical to Republicans' cause.

"Shutting down the government, in my view, is not conservative policy," Mr McConnell told CBS's Face The Nation programme.

"A number of us were saying in July that this strategy could not and would not work - and of course it didn't. So there will not be another government shutdown. You can count on that." Another party Brahmin, former Florida governor Jeb Bush, told ABC that the Tea Party-led shutdown set the party back.

"Tactically it was a mistake to focus on something that couldn't be achieved," said Mr Bush, a centrist known for a pragmatic approach to politics.

"I do a lot of travelling overseas and when we have these political conversations that are not grounded in reality, the rest of the world looks at us as untrustworthy," said Mr Bush, brother of former president George W. Bush, who is said to be an aspirant to the White House as well.

The in-house divisions roiling Republicans have been surprising in a party known for its unity and discipline.

During and even since the crisis, fractious Republicans have seemed almost as much at odds with each other as they have been with Mr Obama.

Longtime conservative activist Richard Viguerie in remarks published on Sunday in the New York Times went as far as to call the infighting a "civil war in the GOP." The party has been hard-pressed to accommodate the libertarian-leaning, conservative Tea Party, which embraces a hardline position that eschews cooperation across party aisles.

Congress late Wednesday gave final approval to a budget compromise that ended a 16-day government shutdown and raised the borrowing limit just hours before the US reached the maximum and could have begun having to default on its bills.

The Tea Party, which spearheaded the revolt against Obamacare, was led in their revolt by upstart Senate Republican Ted Cruz of Texas, who was unrepentant on Sunday, declaring to ABC: "I will do anything and continue to do anything I can to stop the train wreck that is Obamacare."

The Tea Party does not represent a majority of the US electorate, or even most Republicans, but their numbers are sufficiently large to influence elections and stall legislative initiatives when they march, as they almost always do, in lockstep.

The GOP tried on Sunday to pivot attention back to their opposition against Obamacare, but they were still were distracted by having to address frequent questions about party unity.

In addition to slamming the Tea Party, centrist Republicans also have had unkind words in recent days for the conservative Heritage Foundation.

The think tank has been funding many of the Tea party's efforts and candidates - including giving its backing to a hardliner who will challenge Republican Senate leader McConnell.

Even conservative stalwart Senator Orrin Hatch said last week that the powerful think tank "is in danger of losing its clout and its power around Washington, DC."

The budget deal put off a more definitive resolution to the nation's spending battles, with Mr Cruz and other Tea Party conservatives failing to rule out more brass knuckle tactics - including possibly another shutdown - rather than yielding to Democrats' wishes.

"We didn't win this battle, but I am encouraged that we have demonstrated when the American people stand up, the House of Representatives will listen and I hope in time the Senate will listen also," Mr Cruz said.