"Hold me accountable for the debacle," Sebelius responded. "I'm responsible."
Rep. Henry Waxman of California, the ranking Democrat on the committee, scoffed at Republican "oversight" of a law they have repeatedly tried to repeal.
"I would urge my colleagues to stop hyperventilating," said Waxman. "The problems with HealthCare.gov are unfortunate and we should investigate them, but they will be fixed. And then every American will have, finally have, access to affordable health insurance."
The website HealthCare.gov was intended to be the online gateway to coverage for millions of uninsured Americans, as well those who already purchase their policies individually. Many people in the latter group will have to get new insurance next year, because their policies do not meet the standards of the new law.
Throughout the 3 1/2-hour hearing, Sebelius was respectful, often addressing lawmakers as "sir" or "congresswoman." She kept her cool as some lawmakers repeatedly cut off her answers. But she did not shy a few times from tersely interjecting her views while a member was speaking.
The standing-room-only hearing room was silent when she swore an oath to tell the truth and began her opening statement.
Addressing consumers who've tangled with the confusing system, Sebelius added, "So let me say directly to these Americans, you deserve better. I apologize."
She parried questions about problems with the website as well as a wave of cancellation notices hitting individuals and small businesses who buy their own insurance. Those notices are coming because many existing individual policies are too skimpy to meet the law's requirements. The administration says consumers affected will be able to find better coverage.
Lawmakers also wanted to know how many people have enrolled in plans through the health insurance marketplaces. Sebelius stuck with the administration response, promising to release the data in mid-November.
Starting Jan. 1, most Americans will be required to carry health insurance or face fines. At the same time, insurance companies will no longer be able to turn away people in poor health. The law provides subsidized private insurance for middle-class people who don't get health care on the job. Low-income people can access an expanded version of Medicaid in states that agree to expand that safety net program.
Congressional Republicans have introduced competing versions of legislation to let insurance companies continue selling coverage that has been available, freeing them from a requirement to cancel policies that do not meet the standards established in the law.
One bill in the House, authored by Rep. Fred Upton of Michigan, would cover the sale of policies providing individual coverage through 2014.
Republican officials said the House was likely to vote on the issue next month.
Sens. Ron Johnson of Wisconsin and Marco Rubio of Florida back Senate legislation that would apply to existing individual or group policies, and would permit their sale indefinitely. It was not clear if or when a vote might be held in the Democratic-controlled Senate.
Identical legislation has been introduced in the House by Rep. Ron DeSantis, R-Fla..