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“If these concerns are not addressed, consumers may pay a tax for failing to buy insurance primarily through a website that will not permit them to do so,” wrote the attorneys general, led by West Virginia’s Patrick Morrisey.

Sen. John Cornyn, Texas Republican, told Mrs. Sebelius he feared that “navigators” — in-person assisters charged with helping people enroll through Obamacare — are not being fully vetted.

“So a convicted felon could be a navigator and could acquire sensitive personal information from an individual, unbeknownst to them,” he said at the hearing.

“That is possible,” Mrs. Sebelius said. “We have contracts with the organizations, and they have taken the responsibility to screen their individual navigators and make sure that they are sufficiently trained for the job.”

Mrs. Sebelius should appear before the committee each month, for six months, while a tech team tries to repair the website, said Sen. Orrin G. Hatch of Utah, the finance panel’s ranking Republican.

The Centers for Medicare and Medicaid Services said HealthCare.gov was performing slowly Wednesday but had not suffered outages.

Officials also confirmed that CMS chief information officer Tony Trenkle, who had oversight of HealthCare.gov, will leave the agency this month.

Spokeswoman Julie Bataille told reporters on a daily conference call that he was not forced out because of the website’s problems.

“Tony made the decision that he was going to move to the private sector,” she said.