WASHINGTON — President Obama’s three nominees to run Medicare and Medicaid, the Energy Department and the Office of Management and Budget sailed through their separate Senate confirmation hearings on Tuesday and appeared to be on track to win approval from the committees, though none of the panels voted on the nominations.

Marilyn B. Tavenner, who has been chosen to run the government’s big health care programs, won endorsement from the House Republican leader, Representative Eric Cantor of Virginia, who said he had worked with her in his days as a state lawmaker.

Ms. Tavenner deflected criticism of Mr. Obama’s health care policies with mild-mannered responses in which she described herself as a pragmatist committed to solving problems, not scoring ideological points.

She has been acting administrator of the federal Centers for Medicare and Medicaid Services since December 2011. and, if confirmed, would get the job on a permanent basis.