WASHINGTON — An influential GOP senator said Health and Human Services Secretary Kathleen Sebelius should resign over the "disastrous rollout" of the national health care law.

As the top official overseeing the implementation of the troubled HealthCare.gov website testified before a House committee, Sen. Lamar Alexander, R-Tenn., on Tuesday called for Sebelius to step down.

"Expecting this secretary to be able to fix what she hasn't been able to fix during the last three and a half years is unrealistic," Alexander said on the Senate floor. "It's throwing good money after bad. It's time for her to resign, someone else to take charge. No private-sector chief executive would escape accountability after such a poor performance."

STORY: Health official apologizes for website

Alexander joins other GOP lawmakers, including Sen. Pat Roberts of Kansas, in calling for Sebelius to resign. President Obama is standing by Sebelius, a former Kansas governor, and White House spokesman Jay Carney said she enjoys the president's "full confidence."

Sebelius can expect tough grilling on Wednesday when she faces the House Energy and Commerce Committee, in her first congressional testimony since the website's problems came into focus.

Lawmakers from both parties — including some vulnerable Senate Democrats up for re-election next year — have called on the Obama administration to extend the open enrollment period under the health care law while the website is being fixed.

Alexander is the top Republican on the Senate Health Committee, and is respected by Democrats because of his previous tenure as Tennessee governor and a Cabinet secretary. Like Roberts, Alexander is up for re-election in 2014 and faces GOP primary opponent from his right.

Marilyn Tavenner, director of the Centers for Medicare and Medicaid Services, the agency charged with running HealthCare.gov, apologized to the House Ways and Means Committee that "the website has not worked as well as it should."