About 365,000 U.S. residents have signed up for new health insurance through HealthCare.gov and other means, the U.S. Department of Health and Human Services announced, but Republican lawmakers questioned whether millions of people would lose existing coverage by Jan. 1.

Health coverage enrollment numbers rose significantly in November, HHS Secretary Kathleen Sebelius told a congressional committee Wednesday, but enrollments are running far behind HHS projections made before the flawed Oct. 1 launch of HealthCare.gov.

HHS is seeing “very, very positive trends” with enrollments, Sebelius said during a U.S. House of Representatives Energy and Commerce Committee hearing. “There is tremendous interest,” she said. “They’re eager for information, and they’re desperate, many people are, for affordable coverage that they’ve never had before in their lives.”

Sebelius agreed with lawmakers that the troubled launch of HealthCare.gov has led to a slower-than-expected enrollment pace, with internal projections from September expecting 3.3 million people to enroll in insurance coverage by the end of the year.

Asked if she should have delayed the launch of HealthCare.gov, Sebelius declined to offer a direct answer, but said that in hindsight she would have liked more time for testing the website. The first weeks of HealthCare.gov ended up being “beta testing,” she said. “I certainly wish we could’ve saved millions of people a very frustrating experience, and had a smoother technology launch.”

Republican lawmakers questioned whether more U.S. residents would lose coverage than sign up as the Affordable Care Act forces insurance carriers to dump some plans that don’t comply with coverage requirements. Throughout the year, President Barack Obama promised that people who liked their current plans could keep them under the law, but Republicans have pointed to estimates that more than 5 million U.S. residents will lose old coverage.

”We are at a point where, come Jan. 1, 2014, millions more people will have lost coverage than signed up because of the health care law,” Committee Chairman Fred Upton, a Michigan Republican, said earlier this week. “Of all the Americans who have been affected by the law, the vast majority are now without health coverage this holiday season and worried if they will be able to afford a new plan.”

Democrats on the committee disputed the Republican numbers, saying many people are finding better coverage for cheaper prices through the new plans available through the Affordable Care Act. Some Republicans have demanded that their constituents be allowed to keep health insurance that doesn’t cover hospitalization, said Representative Frank Pallone, a New Jersey Democrat.

”I think it’s absurd to keep arguing over these lousy, skeletal plans,” he said.

Several Republican members of the committee also raised concerns that some enrollees wouldn’t have the coverage they expect Jan. 1 because HHS is still working on some back-end functionality at HealthCare.gov. Work continues on some functionality, Sebelius said, but she said she’s confident coverage will be available Jan. 1.

Through the end of November, nearly 365,000 people enrolled through HealthCare.gov, state insurance websites, call centers and other means, with the number of enrollees in November four times the number in October, HHS said. About 39.1 million people have visited the state and federal sites. The agency didn’t break down how many people applied for health insurance through HealthCare.gov.

Since Oct. 1, 1.9 million U.S. residents have completed the coverage eligibility process but have not yet selected an insurance plan, Sebelius said. An additional 800,000 U.S. residents, through their applications, were found eligible for Medicaid or the Children’s Health Insurance Program in October and November.

Some lawmakers accused HHS of not giving them the most relevant numbers because many health insurance enrollees have not yet paid the premiums for their new plans. Payments from enrollees aren’t due until the end of the month, and HHS doesn’t yet have an estimate of the number of people who’ve paid the premiums, Sebelius said.

At one point in the hearing, Representative Michael Burgess, a Texas Republican and former doctor, suggested enrollees are confused about paying for the plans they’ve signed up for. Burgess said he was unable make a premium payment through HealthCare.gov.

”You make a payment to an insurance company, you don’t pay the federal government,” Sebelius said. “You make the payment directly to the insurance.”

Burgess asked if HHS will guarantee that enrollees visiting health-care providers in early January will be covered. HHS says people will be covered Jan. 1 if they sign up by Dec. 23, but what if “you never write the check, you never make the payment?” Burgess said.

”Then you’re not covered,” Sebelius said. “We tell people over and over again they are enrolled when they make a payment. We turn their name over to the insurance company.”