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(CNN) -- Before it even launched, red flags went up about the Obamacare website. Health insurance companies complained about it, and the site crashed during a test run. But nobody told the President of any of it, the nation's health chief told CNN.

Kathleen Sebelius said President Barack Obama didn't hear that there may be problems with the sign-up portal for his signature health care law until it went live on October 1. That's when the site nosedived into a technical abyss.

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In an exclusive interview with CNN's Dr. Sanjay Gupta, the Health and Human Services secretary admitted that her department and the White House are displeased with the technically botched website's rollout.

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"No one could be more frustrated than I am and the President," she said.

The site was supposed to make it simple for people to search and sign up for new health care policies, but instead it's been clunky and, at times, inoperable. And for Sebelius, that's disappointing.

"We're not at all satisfied with the workings of the website," she said. "We want it to be smooth and easy and let consumers compare plans."

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Bringing the 'A-Team'

A team of high-tech experts from within the government and from Silicon Valley is going to tackle the issues, Sebelius said. Jeff Zients, acting director of the Office of Management and Budget, will lead the team.

So why weren't they brought in before the website launched October 1?

"We (had) hoped that they had their 'A-Team' on the table" from the start, Sebelius said of the contractors and agencies responsible for the project.

But now, she said, "we want new eyes and ears. We want to make sure that we get all the questions on the table, that we get all the answers and accelerate the fix as quickly as possible."

The secretary attributed some problems to "extremely high" volume, saying nearly 20 million people came to the Obamacare website in the first three weeks after its launch. Yet only 500,000 people have created accounts on the website. And not all of them have necessarily enrolled in health care plans.

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It's not like no one saw this coming. When the website crashed during a test run, just a few hundred users were on it.

But the Obama administration went ahead with the launch. Waiting was not an option, Sebelius said.

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"There are people in this country who have waited for decades for affordable health coverage for themselves and their families," she said.

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A political lightning rod

Sebelius' comments struck some Republicans as surprising and even odd.

"At this point, she has a lot of questions to answer, and we look forward to her testimony in the House next week," said Brendan Buck, a spokesman for House Speaker John Boehner.

A Senate GOP leadership aide called the situation "odd."

"Everyone was surprised by her statement that the President was unaware of the website's failures until a few days into it," the aide told CNN.

"They had been claiming that the Obamacare rollout was his top priority and that he was receiving regular updates, which was inaccurate. And he gave remarks on October 1 about how great it was and that people should go sign up," the aide said. "Assuming that he didn't know that the website didn't work, why did they let him make that speech when they knew it had crashed in testing? Did really no one recommend a delay to the President? It just seems odd."

Before the website's launch, Republicans made targeting the program a centerpiece of their agenda. Many insisted they wouldn't vote to fund the entire government unless Obamacare was defunded or delayed.

They said that the website's woes show that the Obama administration and the federal government generally aren't capable of executing what the GOP says was an ill-advised program from the get-go.

"God only knows how much money they've spent, and it's a failure," Mitch McConnell, the Senate minority leader, said Sunday on CBS. "The government isn't going to be able to get this job done correctly."

On the other side, Democratic Sen. Jeanne Shaheen of New Hampshire sent a letter to Obama asking that the open enrollment period be extended past March 31, 2014. She also asked that he consider delaying assessment of a penalty to those who don't sign up for any health insurance before the so-called individual mandate kicks in.

Even Obama has been critical, insisting Monday that there's "no excuse for the problems." But he also said the problems should not amount to a blanket condemnation of the Affordable Care Act.

"Nobody's madder than me about the website not working as well as it should," Obama said, "which means it's going to get fixed."

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Calls for resignation

Several top Republicans -- including 2012 vice presidential nominee Rep. Paul Ryan -- have called on Sebelius to step down due to the program's problems. The secretary skirted questions Tuesday about whether she'd step down, saying only that she works "at the pleasure of the President" and is committed to her job.

"I think my job is to get this fully implemented and to get the website working right," she told Gupta.

Billionaire investor Warren Buffett stood up for Sebelius in an interview with CNN's Piers Morgan on Tuesday night.

"I am a friend of Kathleen's, and I'm a friend of her when she's in trouble," he said. "I like Kathleen. I feel sorry for her in the position she's in. Obviously, it's a huge screw-up, but it will get worked out."

Sebelius refused to give a timetable Tuesday as to when the website will be fully operational, but she insisted it's improving every day.

"More people are having an easier time," she said, "and we intend to stay at this until we open the doors wide open."

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And it's too early to call the rollout a failure, the health secretary said. There's still a long time for people to take advantage in person, by calling or by using the website during the open enrollment period.

When that six-month stretch is over, Sebelius said, people can better decide whether this part of Obamacare is a success or a failure.

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CNN's Ben Brumfield and Lateef Mungin contributed to this report.

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