(Bloomberg) -- A day after her deputy apologized for the botched Obamacare exchange, U.S. Health Secretary Kathleen Sebelius will have to stare down accusations that she wasn’t forthcoming enough about the potential problems.

Republicans say they primarily want to know at a hearing today about the lack of transparency ahead of the rocky Oct. 1 debut of the insurance exchange, which is supposed to let people compare and buy health plans. Rep.Paul Ryan of Wisconsin and others are going further and calling for Sebelius to be held accountable for the flaws and to resign.

“This is one of the more difficult assignments that anybody in the Obama administration has undertaken,” says Steve Ryan, a partner at the law firm McDermott, Will & Emery LLP in Washington who counsels people who have to testify to Congress. “Sebelius is about to really earn every nickel of her pay.”

Marilyn Tavenner, the administrator for the Centers for Medicare and Medicaid Services, appeared before a House committee yesterday and blamed outside contractors for the website woes, though she apologized to Americans for the exchange’s flaws. Sebelius plans to tell a separate committee today that she is working to correct the technology issues that have made it hard for people to enroll in coverage.

“She needs to exude confidence about the ability of a technical fix to make a difference -- and to be clear about whether this is the only immediate problem,” says Sarah Binder, a political science professor at George Washington University.

More than 30 House Republicans and at least three U.S. senators are asking for Sebelius to step down. They include Sens. Pat Roberts of Kansas and John Barrasso of Wyoming, as well as Ryan, the Republican vice presidential candidate in 2012 whose losing campaign promised to repeal the Patient Protection and Affordable Care Act if elected.

“The bottom line is the problems with Obamacare run deeper than just the website,” House Majority Leader Eric Cantor, a Virginia Republican, said yesterday at a news conference.

Joanne Peters, a spokeswoman for the Health and Human Services Department, said many of those calling for Sebelius to quit have long opposed the Affordable Care Act.

“There has been a longstanding political opposition to the law by some, despite the benefits it is delivering to millions of Americans,” Peters said in an e-mail. Sebelius “is committed to getting this right and ensuring that healthcare.gov is working smoothly.”

No Democrat has publicly questioned Sebelius’s leadership despite the exchange being plagued by delays and error messages that have prevented some people from completing applications. A few days ago, the data hub that routes tax information to sites run by the federal government and 14 states lost connectivity after workers tried to replace a broken networking component.

In the lead-up to this month’s rollout, Sebelius gave few hints of anything wrong, telling a House committee in June that the online marketplace would be ready. Sebelius plans to tell the House Energy and Commerce Committee today that the “experience on healthcare.gov has been frustrating for many Americans.”

“By enlisting additional technical help, aggressively monitoring errors, testing to prevent new issues from cropping up, and regularly deploying fixes to the site, we are working to ensure consumers’ interaction with healthcare.gov is a positive one, and that the Affordable Care Act fully delivers on its promise,” Sebelius said in prepared remarks for the hearing.

Three of the Republicans who have called for Sebelius to resign sit on the committee. Spokesmen for Reps.Mike Pompeo of Kansas and Phil Gingrey of Georgia said they weren’t sure whether their bosses would ask Sebelius to resign in person. Rep. Pete Olson of Texas plans to focus on what went wrong with the exchange debut.

“He plans to ask questions about the rollout and try to get answers for the America people,” Olson’s spokeswoman, Melissa Kelly, said in an e-mail.

The lawmakers were among 32 House members who wrote to Obama on Oct. 23 asking the president to demand Sebelius’s resignation. In a media briefing the same day, House Speaker John Boehner said someone needs to be held accountable, though he didn’t mention Sebelius by name.

Sebelius, a 65-year-old former Kansas governor, has been relentless in promoting the law, created to provide health coverage for many of the 48 million uninsured Americans. She has made multiple visits to Arizona, Florida, Illinois, Ohio, Pennsylvania, New Jersey, Missouri, Georgia and Texas.

Sebelius has been health secretary since Obama took office in 2009 and has “got to be exhausted,” Steve Ryan said.

“I think what you’d want to do is solve this problem and then leave at an appropriate time under your own power,” he said. “I don’t think the White House is going to dump her because a bunch of people in Congress are screaming about her.”

Tavenner said an “initial wave of interest stressed” the exchange website. She wouldn’t say how many people may have been shut out because of the flaws. She did say enrollment numbers for the main site would be released in mid-November and the delayed Spanish-language and small-business versions of the exchange would be online by the end of November.

“We are seeing improvement each week,” Tavenner told the House Ways and Means Committee. The agency relied on “private sector contractors, just as it does to administer aspects of Medicare. Unfortunately, a subset of those contracts for healthcare.gov have not met expectations.”

President Barack Obama last week appointed Jeffrey Zients, his incoming chief economic adviser, to first advise the health department on fixes to the system before taking on his other job. The federal website, which Zients declared “fixable,” serves consumers in 36 states, including Texas and Florida. He said the site should be running smoothly by the end of November.

That would mean two months when the consumer website at the heart of the $1.4 trillion U.S. health care overhaul won’t be fully operating.

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