* Obama shakes up economic team to tackle growth
* Sperling replacing Summers as Obama adviser
* Obama to promote Furman to number two at NEC (Recasts with Obama remarks, business reaction)
By Alister Bull
WASHINGTON, Jan 7 (Reuters) - President Barack Obama reshaped his economic team on Friday, picking another veteran of the Clinton administration in a staff shake-up aimed at driving the U.S. recovery and winning re-election in 2012.
Obama named Gene Sperling as the new head of his National Economic Council in remarks after a report showed the country's jobless rate had declined last month but still remained high.
"He is a public servant who has devoted his life to making this economy work," Obama told several dozen workers at the Thompson Creek Window Co. in Landover, Maryland.
U.S. unemployment dipped to 9.4 percent last month from 9.8 percent in November, the Labor Department reported on Friday, while the economy created 103,000 new jobs, which was fewer than analysts had expected.
Sperling's pick to replace Larry Summers at the economic council follows Obama's naming of a new chief of staff and the departure of his press secretary, as the president shakes up his team after Republicans took control of the House of Representatives this week.
The NEC coordinates economic policy across the administration and its head wields great influence within the White House. Summers who also served President Bill Clinton as Treasury Secretary, was seen as providing key advice to Obama during the depths of the 2008-2009 financial crisis.
Sperling, a counselor to Treasury Secretary Timothy Geithner, served as head of the NEC for Clinton between 1997 and 2000, and helped Clinton battle the Republicans and, eventually, balance the budget.
"He helped formulate the policies that contributed to turning deficits to surpluses and a time of prosperity and progress for American families in a sustained way," Obama said.
The Business Roundtable, an association of U.S. chief executives, welcomed Obama's choice and said Sperling brought both experience and expertise to the post.
"With the serious economic challenges our nation continues to face -- high unemployment, growing deficits and slow growth -- Business Roundtable looks forward to working collaboratively with Mr. Sperling and policymakers from both parties," it said in a statement.
Obama, who must boost growth to ease U.S. unemployment or be punished in the 2012 presidential election, on Thursday tapped another former Clinton aide, William Daley, an executive at JPMorgan Chase & Co (JPM.N), as his chief of staff.
Press Secretary Robert Gibbs also plans to step down early next month to become an outside adviser to Obama's re-election campaign.
The changes, as Obama enters the second two years of his term, reflect the White House's need to adapt to the new balance of power in Washington after Republicans won big against Obama's Democrats in the November elections.
Republicans tapped into public fury over government spending and a $1.3 trillion budget deficit, and vow to use their increased congressional muscle to undo Obama's healthcare reform program and curb federal borrowing.
Obama, who says he expects a tough debate over spending and taxes, late last year enlisted another old Clinton hand when he picked Jack Lew to lead the Office of Management and Budget.
In addition to Sperling, Obama announced the promotion of Jason Furman to the number two slot at the NEC, the official said. Obama also said he would nominate Katharine Abraham to the White House Council of Economic Advisers and Heather Higginbottom as deputy director of OMB. Both will need confirmation by the U.S. Senate.
(Additional reporting by Patricia Zengerle and Steve Holland, Editing by Anthony Boadle and Paul Simao)