WASHINGTON — President Barack Obama’s top health care official told Congress on Wednesday that she’s responsible for the “debacle” of cascading technical problems that overwhelmed a government website intended to make shopping for health insurance clear and simple.

“Hold me accountable for the debacle,” Health and Human Services Secretary Kathleen Sebelius said during a contentious hearing before the powerful House Energy and Commerce Committee. “I’m responsible.”

Sebelius is promising to have the problems fixed by Nov. 30, even as Republicans opposed to Obama’s health care law are calling in chorus for her resignation. She told the committee that the technical issues that led to frozen screens and error messages are being cleared up on a daily basis.

But even as she started her testimony, some consumers trying to log into the federal website that serves 36 states were getting this message: “The system is down at the moment. We are experiencing technical difficulties and hope to have them resolved soon. Please try again later.”