During the question-and-answer period, Democrats on the panel urged their colleagues -- Democrats and Republicans -- to be patient and work together.
"We can't get caught up in the glitches and technical difficulties and lose our perspective," said Rep. Jim McDermott (D-Wash.).
But Republicans pressed Tavenner for assurances that the website would be ready in plenty of time for people to enroll for coverage, especially those whose health insurance policies have been cancelled because their health plans don't meet new criteria under the Affordable Care Act.
Dec. 15 is the deadline for enrolling for coverage that takes effect Jan. 1.
"Can you guarantee no American will experience a gap in their health care?" Rep. Kevin Brady (R-Texas) asked the Medicare and Medicaid chief.
Those individuals can transfer to new coverage through their insurer or go on the federal exchange, Tavenner explained. Anyone facing a gap in coverage in January "can go to the call center today and we can help them," she said.
During a news conference Tuesday afternoon, Julie Bataille, a spokeswoman for the Centers for Medicare and Medicaid Services, said, "We are confident that consumers will be able to enroll in coverage by December 15th for coverage in January."