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Rep. Steve Stockman, Texas Republican, said Tuesday he will invite to the State of the Union address a 21-year-old Georgia man who became an instant celebrity for claiming to have successfully navigated the buggy federal website — only to explain later that he had not enrolled in a plan.

Other House Republicans demanded enrollment figures from Mrs. Sebelius.

“For the last 3 years, the administration repeatedly promised that everything was ‘on track’ for enrollment, but widespread reports of website failures and the administration’s lack of transparency suggest otherwise,” said House Energy and Commerce Committee Chairman Fred Upton, Michigan Republican. “Although the administration was quick to boast how many people visited their website the first week, they have been silent on the most important numbers of all, enrollment.”

A mixed outlook

Ms. Kaufman, a documentary filmmaker who had coverage until several months ago from a job she held abroad, said she has multiple young-adult friends who are not taking steps to gain insurance.

She refuses to espouse that attitude and is getting by with an expensive, stopgap form of coverage known as COBRA.

The Obama administration is hoping that younger people sign up for health care coverage through the president’s reforms, assuming the markets become fully functional. Healthy customers would balance out the expected enrollments of greater numbers of older and sicker consumers with pre-existing conditions who no longer can be denied coverage under the law.

Republicans say the administration is asking young people to subsidize other people’s health care, but supporters of the law argue that taxpayers already pick up the tab for uninsured Americans who use the emergency room as their go-to doctor’s office.

Ms. Kaufman said she probably will opt for a silver-level plan that costs $250 to $300 per month, although she is not sure what kind of income-based subsidy she might get because she hasn’t been able to make it through the website’s step-by-step enrollment pages.

She thinks she will be able to get through the process eventually, but she said someone who already is skeptical of the law or has dire medical needs might not have a rosy outlook.

“It wasn’t the end of the world to me,” she said. “But I can imagine for someone in a different situation, that could be super-frustrating and really scary.”

Mr. Tassey isn’t bullish about Obamacare’s future.

“I think it’s going to come apart at the seams,” he said. “They enacted it too fast. They didn’t check it out first to make sure it worked.”