Ms. Sebelius told lawmakers on the House Energy and Commerce Committee that she was as surprised as anyone when the website collapsed on Oct. 1 under pressure from millions of users and was crippled by technical problems in subsequent days. While she was aware of the risks in a big information technology project, she said, “no one indicated that this could possibly go this wrong.”

Ms. Sebelius told the committee: “Hold me accountable for the debacle. I’m responsible.”

The shift in strategy from the White House comes as new challenges emerge for the law. The problem-plagued website crashed again just before Ms. Sebelius began testifying in front of a skeptical congressional panel. And officials acknowledged that the federal insurance marketplace for small businesses, which had already been delayed a month from Oct. 1, would not open until the end of November.

In three and a half grueling hours of testimony, Ms. Sebelius gamely defended the troubled rollout of the law and apologized for what had gone wrong. But nothing she said could overcome the stark message displayed on a large video screen showing a page from HealthCare.gov: “The system is down at the moment. We are experiencing technical difficulties and hope to have them resolved soon. Please try again later.”

Representative Mike Rogers, Republican of Michigan, said the administration had not properly tested the security of the insurance website, which receives financial information on consumers seeking subsidies to help pay their premiums.