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Mr. Cantor told the Associated Press in November that Ms. Tavenner was “eminently qualified” to run the agency.

“I would hope to be able to support her,” Mr. Cantor was quoted as saying. “Obviously, I’m not in the Senate, so I don’t have that vote, but I do think she is qualified. Obviously, she’ll be working for a president with an agenda that’s quite different from mine.”

After the White House announced the Tavenner nomination, Sen. Orrin G. Hatch, Utah Republican and ranking member of the Senate Finance Committee, said the Senate would “thoroughly examine” the nomination.

“Any nominee to a federal agency with this much power and authority over the lives of millions of Americans must be carefully scrutinized,” he said. “Republicans on the Finance Committee look forward to examining her record and gaining an understanding of her views on Medicare, Medicaid and the president’s health law.”

Ms. Tavenner isn’t the only nominee to join the administration with a hefty separation package from the health care industry.

Thomas Strickland, chief of staff at the Interior Department, reported a $2 million bonus on disclosure forms for his work at UnitedHealth Group before his nomination hearing. He was one of three top corporate officers who received more than $5 million from the company in 2008, according to Securities and Exchange Commission filings.

He sailed through his Senate confirmation hearing months earlier with no mention of his bonus.