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."
Democratic Rep. Bill Pascrell of New Jersey lambasted Republicans on the panel for choosing to pile on the website woes in their continuing attempt to dismantle the ACA instead of working with Democrats to improve settled law.
Citing the political battle last decade over the Bush administration's Medicare prescription drug benefit opposed by Democrats, Pascrell noted "we lost the policy fight" then but chose to help make the program work instead of trying to discredit or undermine it.
Standing up and pointing at his GOP colleagues, Pascrell shouted: "How many of you stood up to do that? None. Zero. Zero."
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 ACA's website until after its troubled launch on Oct. 1. This was despite the fact that insurance companies had been complaining and the site crashed during a pre-launch test run.