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Earlier this month, a CBS-New York Times survey found 41 percent of adults approve of Mr. Obama’s handling of the economy; 51 percent said they disapproved. Six in 10 Americans said the president has not made progress in dealing with the economy he inherited.

Republicans on Tuesday appeared to hold their fire on Mr. Summers personally, but expressed hope that the personnel change might produce policy shifts as well, notably an end to White House opposition to an extension of Bush-era tax cuts for all taxpayers, including the highest tax brackets.

“We hope this will be followed by an announcement that the White House is ready to work with Republicans to cut spending and stop the president’s tax hike,” said Michael Steel, a spokesman for House Minority Leader John A. Boehner. “Until that happens, the White House is not focused on the No. 1 issue on the minds of the American people: jobs.”

Mr. Summers is only the latest economic adviser to depart the White House. Christina Romer, the former head of the Council of Economic Advisers, left earlier this month. Former Office of Management and Budget Director Peter R. Orszag was the first member of Mr. Obama’s Cabinet to step down when he left in late July.

Mr. Obama recently tapped CEA economist Austan Goolsbee to replace Ms. Romer, while the Senate is making progress on the confirmation of Jacob Lew, nominated to replace Mr. Orszag. The Homeland Security and Governmental Affairs Committee unanimously signed off on his nomination Tuesday.