WASHINGTON (CNN) -- Out of the political frying pan and into the partisan fire for Health and Human Services Secretary Kathleen Sebelius.

A day after apologizing and taking responsibility for the problem-plagued Obamacare website, Sebelius got subpoenaed on Thursday by one of the fiercest Republican critics of the administration -- House Oversight Committee Chairman Rep. Darrell Issa of California.

The subpoena demands documents and information relating to the HealthCare.gov website, a spokesman for Issa's committee told CNN's Lisa Desjardins.

It's been almost a month since the website for enrolling in President Barack Obama's signature health care reforms went live. But technical problems, despite a series of advance warning signs, have impeded the system and provoked anger and frustration.

Even after a chorus of apologies out of Washington, it may be another month before everything's running smoothly.

Vice President Joe Biden became the highest-ranking administration official to apologize on Wednesday for the botched rollout.

"We assumed that it was up and ready to run," he told CNN's sister network HLN. "But the good news is although it's not -- and we apologize for that -- we are confident by the end of November it will be, and there'll still be plenty of time for people to register and get online."

That mea culpa came after Sebelius apologized for the "miserably frustrating" problems during a 3 1/2-hour congressional grilling. She said she made a mistake when she told Obama that HealthCare.gov was "ready to go" for its October 1 launch.

Sebelius promised a "vast majority" of consumers will have an easier time shopping online for health insurance under Obamacare by the end of November.

"In these early weeks, access to HealthCare.gov has been a miserably frustrating experience for way too many Americans, including many who have waited years, in some cases their entire lives, for the security of health insurance," Sebelius said.

She echoed the overall administration stance -- that a team of experts is scrambling to fix the website's errors.

To the frustrated users who have had problems, she said: "You deserve better. I apologize. I'm accountable to you for fixing these problems."

Obama tried to log on

Biden said he didn't even bother logging on to the Obamacare site.

"Actually, the President tried to get online, and my daughter tried to get online," he said. "I did not, because it was clear that I was not getting online."

Obama himself acknowledged that too many people "have gotten stuck, and I am not happy about it."

"There's no excuse for it," the President said. "And I take full responsibility for making sure it gets fixed ASAP."

Glass half full?

Sebelius said the sweeping health care program has delivered on its promise to provide affordable health care coverage. Thousands have been able to access the website to look at new health coverage options that will give them security of knowing they won't go bankrupt if they get sick, she said.

Republicans have called for Sebelius to be fired for the Obamacare problems, but a White House spokesman said Wednesday that Obama has "complete confidence" in her.

"She took responsibility for many of the problems that are evident with the (Obamacare) website, but she also deserves credit for the other aspects of the Affordable Care Act implementation that have gone well," spokesman Josh Earnest told reporters.

In fact, Obama tried to turn the tables on Republican opponents of his signature health care reforms, challenging them to come up with helpful ideas instead of undermining the federal law.

"Anyone defending the remnants of the old, broken system -- as if it was working for people -- anybody who thinks we shouldn't finish the job of making the health care system work for everybody ... those folks should have to explain themselves," he said.

According to the Kaiser Family Foundation website, 15.4 million people had individual health care coverage in 2011, representing about 5% of the population. The vast majority of Americans have coverage through their employer, Medicare, Medicaid or other public providers.

White House spokesman Jay Carney said Tuesday that "a significant portion" of the 5% of people with individual coverage will end up paying less for better policies when they shop around in the new exchanges.

Early warning signs

Some of the criticism surrounding the website's launch has to do with what Obama and other officials knew -- and when they knew it.

CNN has learned the administration received stark warnings a month before the launch that the Obamacare site was not ready to go live, according to a confidential report. The caution, from the main contractor CGI Federal, warned of risks and issues for HealthCare.gov, even as company executives were testifying publicly the project was on track.

Sebelius told the House committee the outside contractors who built the website never recommended delaying this month's launch. But she conceded that "we did not adequately do end-to-end testing."

The contracts with the private companies working on the Obamacare website -- which amount to $174 million so far, with more bills due well into 2014 -- do not have "built-in penalties" allowing her department to charge them for disappointing or faulty work, Sebelius said. But Sebelius said the agency will not pay for incomplete work.

Security questions

Republican Rep. Mike Rogers of Michigan, who chairs the House Intelligence Committee, accused Sebelius of putting the private information of Americans at risk by failing to properly test security measures on the website.

"This is a completely unacceptable level of security," he said. "You know it's not secure."

Sebelius responded that testing occurs regularly, and she told Rogers she would get back to him on whether any end-to-end security test of the entire system has ever occurred. Rogers said he knows there have been no such comprehensive security tests.

An internal government memo obtained by CNN on Wednesday that was written days before the website launched warned of a "high" security risk because of a lack of testing.

"Due to system readiness issues, the (security control assessment) was only partly completed," said the Centers for Medicare and Medicaid Services memo. "This constitutes a risk that must be accepted and mitigated to support the Marketplace Day 1 operations."

Sebelius told CNN last week that Obama didn't know of the problems with the site -- even though insurance companies had complained and the site crashed during a pre-launch test run -- until after it went live.

A senior administration official said Obama now gets a "nightly readout" with the latest Obamacare statistics and an update of the website's status.

CNN's Brianna Keilar, Joe Johns, Gloria Borger, Kevin Bohn, Lisa Desjardins and Z. Byron Wolf contributed to this report.