WASHINGTON (CNN) -- For the first time, someone in the Obama administration apologized for the problem-plagued Obamacare website.
But Marilyn Tavenner also insisted Tuesday that the online troubles were being resolved and the overall program was working, albeit slower and less successfully than hoped.
In the first congressional testimony from a government official on the botched launch of HealthCare.gov, the head of the federal Centers for Medicare and Medicaid Services told the House Ways and Means Committee that the "vast majority" of consumers would be able to successfully use the site by the end of November.
"I want to apologize to you that the website does not work as well as it should," she said, adding that HealthCare.gov "can and will be fixed."
At the same time, Tavenner also conceded that some people with individual health coverage -- rather than the group coverage that most Americans have -- will be forced to get new policies because of increased requirements under the 2010 Affordable Care Act.
"These individuals in a small group, our individual markets, had no protections" before the reforms became law, Tavenner explained.
Before the health care reforms, such consumers "could be kicked out any time for pre-existing conditions" or realize too late that their policies failed to cover hospitalization or cancer treatments, Tavenner said. Now, the reforms protect them by requiring a minimum standard of coverage, she added.
For some, that means more expensive policies, and any change breaks the oft-repeated pledge by President Barack Obama that "if you like your plan, you can keep your plan" when he was pushing for Congress to pass his signature reforms.
On Capitol Hill, a top House Democrat told reporters on Tuesday that his party "should have been more precise" when making the pledge about people keeping coverage they liked.
"I think preciseness would have been better" said Rep. Steny Hoyer of Maryland, adding that the promise was made to try to allay the fears of the majority of Americans who get health coverage from their employers or government programs such as Medicare and Medicaid.
According to the Kaiser Family Foundation website, 15.4 million people had individual health care coverage in 2011, representing more than 5% of the population. The vast majority of Americans -- at least two-thirds of the population in 2011 -- had coverage through their employer, Medicare, Medicaid or other public providers and will not be affected by changes involving individual coverage.
As expected, Tuesday's hearing included fiery partisan exchanges, with Republicans saying the website problems foreshadow deeper problems that threaten higher premiums and government intrusion in future health coverage while Democrats accused them of trying to kill reforms that benefit millions of Americans.
Under relentless GOP questioning, Tavenner said initial figures on how many people have enrolled so far for health coverage under the reforms won't be available until mid-November.
She noted that the administration has expected the initial enrollment to be small, but noted that the enrollment period ends on March 31.
When asked by Republicans about the expected initial low enrollment, Tavenner pointed out that a similar dynamic occurred with implementation of the Massachusetts health care law, when people waited until the final deadline approached to sign up.
To GOP Rep. Dave Camp of Michigan, the committee chairman, low enrollment signals the failure of the health care reforms, which need young and less-expensive people to sign up so insurers can offer affordable plans in markets that include older and more-expensive people.
"I fear we can see a fundamental breakdown of the insurance market where premiums will skyrocket, pricing millions of Americans out of health care," he said.
Later, Republican Rep. Kevin Brady of Texas asked Tavenner for a guarantee that consumers will be able to obtain coverage required by the health care law before the deadline.
"What I can guarantee is that we have a system that is working. We are going to improve the speed of that system," she said.
But Brady interrupted her.
"Excuse me," he said. "You are saying the system right now is working?"
Tavenner didn't budge, responding: "I am saying it is working. It is just not working at the speed that we want and at the success rate that we want."
In prepared testimony for the hearing, Tavenner said private contractors hired to create the website "have not met expectations." Asked about that statement, she cited one of the contractors -- CGI Federal, which has a contract worth as much as $200 million for its work on the system.
Tavenner's agency oversaw the creation of the online health insurance marketplace that has taken so much heat.
She reports to Health Secretary Kathleen Sebelius, who has come under fire for the problems that plagued the introduction of the enrollment website.
Some congressional Republicans demand her resignation or firing, and Sebelius will face a hearing by the House Energy and Commerce Committee on Wednesday.
In an exclusive interview with CNN last week, Sebelius said Obama didn't know of the problems with the Affordable Care Act's website until after its troubled launch on October 1. This was despite the fact that insurance companies had been complaining and the site crashed during a pre-launch test run.