"We are seeing improvements each week, and by the end of November, the experience on the site will be smooth for the vast majority of users," she said.
Tavenner said the site would be "fully functioning" by the end of the month.
She seemed reluctant to concede the widespread cancellations some senators referred to.
"Some of the 5 percent of Americans who currently get insurance on the individual market have recently received notices from their insurance companies suggesting that their plans will no longer exist," she said.
"These Americans do have a choice. They can choose a different plan being offered by their insurer or they can shop for coverage in the marketplace or outside the marketplace. As insurers have made clear, they are not dropping consumers; they're improving their coverage options, often offering better-value plans with additional benefits."
Despite her general assurances, several senators raised detailed questions about experiences their own constituents have had.
Sen. Lisa Murkowski, an Alaska Republican, said that as of Monday, only three people in her state had been able to enroll, and she said there were concerns that they had done so on the basis of incorrect information.
Sen. Tim Scott, R-S.C., cited an example of a man whose personal financial information had been disclosed.
Tavenner appeared at a time when Democrats remain uneasy about the implementation of a program they created over unanimous Republican opposition in 2010.
The website went down again in the middle of the day Monday for about 90 minutes. And the administration still refuses to divulge enrollment statistics until mid-November.
Tavenner began her career as a nurse and built a successful record as a hospital executive before entering public service. Seen as a businesslike manager, she has enjoyed support from lawmakers across the political spectrum.
Healthcare.gov was supposed to provide one-stop shopping for people who don't have a health plan through an employer. Its target audience is not only uninsured Americans but those who already purchase coverage individually. Middle-class people can sign up for private coverage made more affordable by tax credits that act like a discount on premiums. Lower-income people will be steered to an expanded version of Medicaid in states that agreed to expand that safety-net program.
A new study released Tuesday estimates the potential size of the market nationally at 28.6 million people. The nonpartisan Kaiser Family Foundation says three out of five people, or more than 17 million people, will be eligible for tax credits. That includes both uninsured people and those switching over from current individual plans. Texas, California and Florida have the highest numbers of residents eligible for the credits.
Earlier, the Congressional Budget Office estimated that 7 million uninsured people would gain coverage through the marketplaces, a statistic the Obama administration adopted as its own enrollment target.