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But several GOP lawmakers have called for Mrs. Sebelius‘ resignation, and website problems have been eclipsed this week by concerns that many Americans in the individual market will not be able to keep their existing health plans, as Mr. Obama had promised.

Chairman Fred Upton, Michigan Republican, said Mr. Obama’s vow has been cast into doubt by a flood of cancellation notices nationwide.

Mrs. Sebelius said if a plan was in place in 2010, when Congress passed the law, then it could have been grandfathered in.

She reminded lawmakers that the individual market covers a small percentage of Americans — many are covered by their employers or by programs such as Medicare — and that some consumers will gain a better health plan at similar or lower cost, through the help of government subsidies.

She also said Americans who were dropped from their current plan must be offered an alternative plan.

Mr. Upton said Americans are “scared” and “frustrated” with the situation, since many of these people cannot use the Obamacare websites to explore their options — mere weeks after Mrs. Sebelius and her lieutenants assured lawmakers the federal exchange system was ready to launch.

Rep. Marsha Blackburn, Tennessee Republican, told Mrs. Sebelius, “you’re taking away their choice.”

“I will remind you,” she said, “some people like to drive a Ford, not a Ferrari, and some people like to drink out of a red Solo cup, not a crystal-stem” glass.