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Health and Human Services Secretary Kathleen Sebelius on Wednesday touted the progress of the federal health care exchange despite new enrollment numbers showing the government is more than 800,000 customers short of its goal.

Updated ObamaCare enrollment numbers were released ahead of Sebelius’ testimony.

The total number of people who signed up for ObamaCare using the federal HealthCare.gov website has grown to 365,000 but still falls way short of the government’s own estimate of 1.2 million sign-ups by this time. Though the numbers show that sign-ups are accelerating since the rocky launch in October, they raise doubt as to whether the administration can hit its original goal of 7 million sign-ups by the end of March.

Sebelius, who testified before the House Energy and Commerce Committee on Capitol Hill, sounded upbeat when asked about HealthCare.gov’s website design, workability and security.

“HealthCare.gov is working faster, responding more quickly, and we’re able to handle larger volumes of concurrent users,” Sebelius said. It was her second appearance before the committee since the marketplace went live Oct. 1. “Pages that once took eight seconds to load are now responding in under a second. The site’s error rate which once topped 6 percent has been driven down to below 1 percent.”

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    According to a new Health and Human Services report released Wednesday, the pace of health insurance sign-ups picked up in November. The number of people who signed up for coverage through the federal website was 137,204, compared with October’s 26,794.

    The 14 states running their own websites enrolled 227,478 people, up from 79,391 in October.

    California, which is running its own program, led the nation, with more than 107,000 sign-ups. Oregon, also running its own market, had the lowest total, with just 44 people enrolled. Florida was the leader among states with federally run markets, with nearly 18,000 sign-ups.

    Rep. Michael Burgess, R-Texas, pressed Sebelius on the difficulty he said he had making a payment on the federal online exchange.

    "Do you know how hard it is to make that payment?" Burgess asked. "To pull your billfold out and make that payment? I will tell you it's almost impossible."

    Burgess said he’s worried people will sign up for a plan but then run into problems during the payment process and ultimately not be to get insurance.

    In a blog post Wednesday morning, Sebelius announced she will ask the department’s inspector general to investigate the contracting process, management, performance and payment issues surrounding the launch.

    Rep. Marsha Blackburn, R-Tenn., brought up concerns published in a Los Angeles Times story that claimed California’s health exchanges leaked names and contact information for tens of thousands of people who went online to check out the California coverage options but did not ask to be contacted.

    Sebelius pointed out that the California exchange is a state exchange and not run by the federal government. She added, “To my knowledge, the California incident is an isolated case. We don’t store personal information on the federal hub.”

    The site went live on Oct. 1 and immediately turned into an impenetrable maze for most consumers. A two-month program of fixes directed by White House troubleshooter Jeffrey Zients stabilized the site and made it more workable, resolving hundreds of software glitches and adding more hardware to handle high demand from consumers.

    Zients also found that the technical problems were compounded by inadequate oversight and coordination among teams working for the government and its contractors. That raises questions about how Sebelius and her subordinates have managed the complex program. Through the summer and into the fall, the secretary had repeatedly assured Congress and the public that the insurance markets would open for business on schedule Oct. 1.

    With his poll ratings in a dive, Obama not only accepted the blame for website woes, but personally apologized for the canceled individual insurance policies. The cancellations issue is highly sensitive politically because it contradicts Obama's promise that if you like your coverage you would be able to keep it.

    The president sought to calm the backlash by allowing states and insurers to extend existing plans for another year. Thirty-eight have done so, according to analysis by the consulting firm Avalere Health. But it's unclear to what extent insurers have taken advantage of the leeway granted by state regulators.

    The administration had set a goal of signing up 7 million people by the end of open enrollment season March 31. HHS health reform director Mike Hash says they're still "on track" to meet it. Uninsured people who procrastinate beyond that date will face tax penalties when they file their returns for the 2014 tax year.

    The Associated Press contributed to this report.