The top Republican on the Senate’s health panel is calling on Kathleen Sebelius to quit, putting fresh pressure on the Health and Human Services secretary as concerns grow over Obamacare. Sen. Lamar Alexander (R-Tenn.), the ranking member on the Health, Education, Labor and Pensions Committee, says President Barack Obama should ask the embattled health secretary to resign because of the “disastrous rollout” of the new health care law.

“At some point there has to be accountability,” Alexander said on the floor. “Expecting this secretary to be able to fix what she has not been able to fix during the last three and one half years is unrealistic. It is throwing good money after bad.”

Alexander, a former governor and Cabinet secretary who is close with Senate Minority Leader Mitch McConnell, is now one of the highest ranking Republicans to call on Sebelius to quit, given that he serves as the top minority member on the committee that shares jurisdiction over health care issues.

Many Republicans have yet to go as far as calling Sebelius to resign, even as they have bashed the Obama administration over the rollout of the new online marketplaces and the requirement for Americans to purchase health insurance.

With Alexander’s announcement, it could encourage more Republicans to begin demanding Sebelius to step aside and pressure red-state Democrats who are up for reelection in 2014 to join those calls.

Indeed, Alexander’s demand is also a sign calling on Sebelius to quit is good politics on the right: the Tennessee Republican faces reelection next year to a third term and is working to solidify his right flank ahead of a primary challenge.

“It is time for her to resign and for someone else to take charge,” Alexander said. “No private sector chief executive officer would escape accountability after such a poor performance. And the principle of accountability is not foreign to the public sector.” Alexander, who joined 30 other Republicans in voting against Sebelius’ nomination to the post in 2009, has stepped up his criticism of the health secretary this year, including after revelations she had urged health industry officials for contributions to help implement the sweeping law.

Now, Alexander says Sebelius has not been forthcoming with Congress about the rollout of the law, including details about Americans who have enrolled in it. “With Wikileaks and Edward Snowden spilling our beans every day, what’s happening on the Obamacare exchanges is the only secret left in Washington,” Alexander said. “The National Security Agency could learn some lessons from Secretary Sebelius.”