Sen. Lamar Alexander (R-Tenn.), the ranking Republican on the Senate health committee, on Tuesday called for Secretary of Health and Human Services Kathleen Sebelius's resignation

“Expecting this secretary to be able to fix in a few weeks what she has not been able to fix during the last three and one half years is unrealistic," Alexander said on the Senate floor. "It is throwing good money after bad.”

Alexander joins a small group of GOP senators -- including Sens. Pat Roberts (Kan.) and John Barrasso (Wyo.) -- and a larger group of House Republicans who have also called for Sebelius's job amid myriad problems with the launch of Obamacare's health insurance exchanges.

In contrast to the group of House Republicans, though, Alexander is known as more of a bipartisan deal-maker than a partisan warrior.

Alexander served in Senate GOP leadership until last year. He has been targeted by some tea party groups in his 2014 primary.

Sebelius last week said that she didn't work for the people who were calling on her to resign.

Sen. Joe Manchin (D-W.Va.), who has been critical of the new health-care law's rollout, on Sunday gave Sebelius a vote of confidence, saying she should remain in the job and that he thought she would right the ship.

Correction: This post previously said Sen. Jerry Moran (R-Kan.) had called for Sebelius to resign. He has instead more generally called for accountability for the problems.