HHS Secretary Kathleen Sebelius told Congress this morning that she has ordered a probe into how the Obamacare insurance exchanges became "flawed and failed and frustrating for millions of people" - in a single word, "unacceptable."

The embattled Health and Human Services secretary also conceded for the first time publicly that, knowing what she now knows, she would not have launched the website nationwide on Oct. 1, as originally planned. "I would have probably done a slower launch, maybe with fewer people, and done some additional beta testing," she testified before the House Energy and Commerce Committee.

"We want to both figure out exactly the chain of events, what went wrong, which is why I've asked the inspector general to help do this investigation," she said of the investigation she has requested. Sebelius put the total IT cost of the website at $677 million through the end of October. Of that, $319 million has been spent so far, she said.

At the same time, citing vast improvements to the online system, Sebelius appealed directly to the millions of frustrated users who were initially turned away. "We are asking you to come back," she said. More than 1.9 million people have completed applications but not yet selected a health plan.

"I don't want to minimize the dampening effect that the flawed technology had not just on the federal website but … also dampened the enthusiasm at the state level," she said. "Having said that, we're seeing very, very positive trends. We're seeing a lot of people re-engage, and it's about not only just the numbers of individuals, but at the end of the day, hopefully getting the right mix of individuals."

HHS is in a race against time to get that mix right, with the enrollment deadline for January coverage coming up on Dec. 23. Sebelius said 1.9 million Americans have applied for coverage but not yet selected plans, for a variety of reasons. More than 365,000 Americans have completed the process, but there's no guarantee that all will have coverage in effect at the beginning of the year.

"Some may have paid, some may have not," Sebelius said of the premiums required to complete enrollment.

"So you can't guarantee the actual number of constituents who have coverage?" asked Rep. Joe Pitts, R-Pa.

"Not until they pay their premium," she said. Premiums are due by Jan. 1 to complete enrollment.

Meanwhile, as many as 35,000 people who think they are successfully enrolled may not be, according to HHS, due to errors in 834 forms that get sent to insurers to complete the process.

"In the early days there were a serious number of errors," Sebelius said. "And we are in the process of actually hand-matching individuals with insurance companies…. We want to go back and make sure that everyone who thinks they are enrolled in the early days actually is matched with a company and that the company folks are matched on our end."