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Sen. Richard C. Shelby, Alabama Republican and ranking member on the Senate’s banking committee, which will hold hearings for Mrs. White and Mr. Cordray, said that he also has concerns about the new agency and that his opposition to Mr. Cordray’s nomination hadn’t changed from two years ago.

Other senators on the banking committee said they plan to question Mrs. White about how her experience as a federal prosecutor will affect her role at the SEC.

Sen. Jon Tester, Montana Democrat, said he is particularly concerned about how she will implement the Jobs Act.

“At a time of great economic potential, too many new businesses and entrepreneurs are waiting for this bipartisan law to be fully implemented,” he said.