By David Lawder and Andy Sullivan

WASHINGTON (Reuters) - U.S. lawmakers launched an effort to resolve budget differences in a less confrontational fashion on Thursday as Washington picked up the pieces from a political crisis that has slowed the economy and undermined the country's international standing.

As hundreds of thousands of federal employees returned to work, Republican and Democratic negotiators held their first meeting to tackle tax and spending issues that have led to repeated rounds of brinkmanship over the past three years.

But one day after Congress ended a 16-day government shutdown and stepped back from the edge of an unprecedented debt default, many feared that they have only set the stage for another standoff in the months to come.

"I just hope we don't have to go through this again in two months," said Sandria Coombs, a contractor at the Environmental Protection Agency who was furloughed.

The last minute budget deal, signed into law by President Barack Obama just after midnight, restores government funding through January 15 and extends its borrowing authority through February 7, though the Treasury Department might be able to stave off a default for several weeks past that point.

Speaking at the White House, Obama urged lawmakers to turn to more productive work. He suggested an ambitious agenda including an overhaul the country's immigration program by the end of the year and resolution of long-term budget issues. He also called for final work on a farm bill that had been sidelined by the fiscal confrontation.

"Let's work together to make government work better instead of treating it like an enemy," he said.

On Capitol Hill, budget negotiators pledged to bridge the vast gulf between Republican and Democratic fiscal priorities. The panel is supposed to reach agreement by December 13, but there are no guarantees it will succeed where similar efforts have failed.

The standoff ended with a clear defeat for Republicans, who had sought to tie government funding to measures that would undercut Obama's signature Affordable Care Act.

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That effort failed, and the standoff diverted public attention away from the administration's sloppy rollout of the health law's online insurance exchanges.

The fight split business-friendly Republicans from grassroots Tea Party conservatives and left the party on the wrong side of public opinion. Though Obama's approval rating fell during the crisis, polls showed that most voters blamed Republicans for the standoff.

A Pew Research Center poll found that 49 percent of Americans now have a negative view of the Tea Party, a new low. But Tea Party groups remained unbowed: several on Thursday endorsed a conservative primary challenger to Mississippi Republican Senator Thad Cochran, who is up for reelection next year.

Republican Representative Tom Cole from Oklahoma, who sits on the budget panel, said it is time to move on. "We've had the fight," he said on MSNBC. "Now it's time to get down and identify the things we can agree on."

U.S. stocks gained on Thursday with the S&P 500 index hitting a record intraday high. The index fell as much as 4 percent during the standoff but recovered as a deal emerged.

WORKERS RETURN

Hundreds of thousands of federal workers who had been idled by the standoff returned to work. Vice President Joe Biden brought muffins to returning workers at the Environmental Protection Agency, while Agriculture Secretary Tom Vilsack greeted workers returning to the agency's headquarters on the National Mall.

Though federal workers will get back pay, the standoff is likely to slow economic growth in the fourth quarter from 2.5 percent to 2.3 percent with a high risk that it could slow even further, according a Reuters survey of 70 economists.

"The insanity in Washington is affecting consumer and business confidence. That's the huge restraint to growth," said Joel Naroff, chief economist at Naroff Economic Advisors in Holland, Pennsylvania.

The standoff has elevated borrowing costs, caused private-sector furloughs and delayed mortgage applications and construction permits. Mark Zandi, chief economist of Moody's Analytics, estimates that it will cost the economy $20 billion.

The last debt-ceiling fight in 2011 depressed consumer confidence for months and raised the United States' borrowing costs by $19 billion over 10 years.

The United States' once-perfect credit rating has been dented by the repeated confrontations. Standard and Poor's downgraded U.S. debt following the 2011 crisis, while Fitch warned on Tuesday that it may cut its assessment as well.

The third major rating agency, Moody's, said on Thursday it would maintain its AAA rating.

One possible upside: the turbulence could prompt the Federal Reserve to keep its massive monetary stimulus in place through next year. One Fed official said the deadlock has undermined the central bank's ability to fight high unemployment.

"Kicking the can down the road for a few months will not solve the pathology of fiscal misfeasance that undermines our economy and threatens our future," Dallas Fed President Richard Fisher told the Economic Club of New York.

Economists say the spending cuts and tax hikes approved by Congress over the past several years have elevated the unemployment rate even as they have helped the country narrow budget deficits.

The deal approved Wednesday is likely to cause more short-term pain by keeping the across-the-board "sequester" cuts in place. Officials at the Pentagon and other federal agencies that have been able to minimize the impact of the cuts so far say they will slice deeper in the months to come.

(Additional reporting by Jeff Mason, Mark Felsenthal, Steve Holland, Susan Heavey, David Lawder, Ian Simpson, and Lucia Mutikani in Washington, and Jonathan Spicer in New York; Editing by Tim Dobbyn)