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Stocks shake off budget, debt concerns; close higher

Stocks finished higher on Friday, recovering from the previous day's sharp losses as the Dow reclaimed its footing above the 15,000-point mark despite the Washington budget stalemate and looming deadline to raise the U.S. debt ceiling.

Still, the Dow and S&P finished in the red for the week. The Nasdaq, meanwhile, closed in positive territory for the fifth-consecutive week.

(Read more: A tweet underscores why Washington is stuck)

"Those looking for another selloff to at least test yesterday's lows were left at the altar," wrote Elliot Spar, market strategist at Stifel NIcolaus. "Bottom-line: This Washington mess will pass; yes, it will have a negative impact on the economy and data releases over the near term but this is temporary.

"The market is able to look over the valley...No, I am not saying throw money at the market," he said. "You still have to be very selective while still using market rallies to hedge your weak technical holdings."

The Dow Jones Industrial Average closed 76 points higher, boosted by Disney and Boeing, after finishing below the 15,000 mark on Thursday for the first time since early September.

The S&P 500 and the Nasdaq also finished in positive territory. The CBOE Volatility Index (VIX), widely considered the best gauge of fear in the market, was unchanged above 17.

All key S&P sectors finished higher, led by materials and health care.

(Watch: Art Cashin: The REAL reason DC's still shut)

"I find it painful to say this, but the government shutdown doesn't tend to affect markets at all," said Scott Clemons, chief investment strategist at Brown Brothers Harriman Wealth Management. "The debt ceiling debate, however, is a different matter. I think people are pricing in the political brinkmanship as 'business as usual' in DC. When push comes to shove, everyone knows the US cannot default on its debt and so some compromise has to be struck…we're likely to have uncertainty until the 11th hour."

Stocks briefly pared their gains after Speaker John Boehner said the House will not vote on a "clean" spending bill without conditions to end the government shutdown, and demanded spending cuts in exchange for raising the government's borrowing limit.

President Obama canceled his trip to Indonesia to attend the APEC (Asia-Pacific Economic Cooperation) conference in order to focus on domestic economic issues.

"But the Republican headbangers hardly look like budging. And in the meantime, the economic disruptions caused by the shutdown both in the U.S. and beyond, and arguably more significantly, the uncertainty and hit to confidence from fears over the debt ceiling not being lifted, will intensify," wrote Chris Scicluna, an economist at Daiwa Capital.

Speaking in Washington, International Monetary Fund chief Christine Lagarde said that a failure to raise the debt ceiling before October 17 could hurt the global economy, and warned that U.S. economic growth could drop below 2 percent this year.

The widely-watched monthly government jobs report was delayed due to the shutdown. About 180,000 jobs were expected to have been added in September, up from 169,000 added in August.

(Read more: 'Squawk Box Jobs Report' pegs job growth at 158K)

"I actually think the bigger story is corporate earnings—that's the fuel that drives the market, not Washington DC," said Clemons.

Third-quarter earnings season kicks off next week, with notable companies including fast-food chain Yum Brands and former Dow component Alcoa slated to post results Tuesday. Financial giants JPMorgan and Wells Fargo are due to report on Friday.