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Health and Human Services Secretary Kathleen Sebelius took a swipe Friday at those calling for her to resign over the botched ObamaCare website rollout, suggesting that Republican efforts to delay and defund the law contributed to HealthCare.gov's glitch-ridden debut.

During a visit to a community health center in Austin, Sebelius conceded that there wasn't enough testing done on the website, but added that her department had little flexibility to postpone the launch against the backdrop of Washington's unforgiving politics.

"In an ideal world there would have been a lot more testing, but we did not have the luxury of that. And the law said the go-time was Oct. 1," she said. "And frankly, a political atmosphere where the majority party, at least in the House, was determined to stop this anyway they possibly could ... was not an ideal atmosphere."

Sebelius said her agency tested the site using five times the maximum traffic ever experienced by Medicare.gov, a similar site. But she said that was a gross underestimate of the demand placed on HealthCare.gov. She also said the high volume not only contributed to its failure, but also exposed other problems.

Republican Texas Sen. John Cornyn questioned why Sebelius was there. "If she's still confused about who exactly she works for and if she hasn't come ready to answer questions about why hundreds of millions of taxpayer dollars have been wasted on a botched product, she might as well not visit," he said in a statement.

Sebelius, instead of testifying at a hearing on Thursday, visited an ObamaCare call center in Phoenix where she also rebuffed Republican calls for her resignation.

"The majority of people calling for me to resign I would say are people who I don't work for, and who do not want this program to work in the first place," she said.

The visits are part of a multi-city tour by White House officials and Cabinet secretaries to "directly reach uninsured Americans." They are hitting up cities with high rates of uninsured, where they will encourage people to sign up.

Yet on the sidelines, the newly hired fix-it team is trying to address major problems with the ObamaCare website. The Republican National Committee mocked Obama for taking the show on the road "while ObamaCare continues to derail."

The House Energy and Commerce Committee held its first hearing on the matter Thursday where four contractors testified -- and claimed that part of the problem was the administration did not allow enough time for testing.

Sebelius will have her turn in the hearing room next Wednesday.

Rep. Fred Upton, R-Mich., chairman of the committee, told Fox News that while contractors were certainly pointing fingers at each other, the problem "goes up the ladder" to HHS.

"This is a serious attempt to figure out what went wrong. And the taxpayers have spent hundreds of millions of dollars trying to develop a system. The administration told us, it was going to work. No problem. They looked us in the eye," he said. "No one knows how this thing is working at all."

On Friday, the administration announced that QSSI, a contractor who worked on the site, was being promoted as a general contractor overseeing the repairs of the entire system. Officials said most issues will be repaired by the end of November.

Hearings aren't Obama's only problem pertaining to the health care law.

Restless Democrats who are running for re-election next year are starting to join Republicans in calling for a delay of the law's individual mandate. They, like Republicans, argue it's unfair to force Americans to buy insurance when the main system to help them is not yet fully operational.

The administration, in response, is stressing that individuals will have until the end of March to enroll. Contractors testified Thursday that the system should be all ready before the start of 2014.

The rest of the cities and regions on the ObamaCare tour are: Dallas, Houston, Miami, Atlanta, Tampa, Orlando, Detroit, and northern New Jersey.

The Associated Press contributed to this report.