WASHINGTON — After focusing for weeks on the technical failures of President Obama’s health insurance website, Republicans on Tuesday broadened their criticism of the health care law, pointing to Americans whose health plans have been terminated because they do not meet the law’s new coverage requirements.

The rising concern about canceled health coverage has provided Republicans a more tangible line of attack on the law and its most appealing promise for the vast majority of Americans who have insurance: that it would lower their costs, or at least hold them harmless. Baffled consumers are producing real letters from insurance companies that directly contradict Mr. Obama’s oft-repeated reassurances that if people like the insurance they have, they will be able to keep it.

“My constituents are frightened,” Representative Kevin Brady, Republican of Texas, told Marilyn Tavenner, the official whose department oversaw the creation of Mr. Obama’s health insurance marketplace, at a House Ways and Means Committee hearing Tuesday. “They are being forced out of health care plans they like. The clock is ticking. The federal website is broken. Their health care isn’t a glitch.”

In the weeks since the health marketplaces opened, insurance companies have begun sending notices to hundreds of thousands of Americans in the individual insurance market informing them that their existing plans will soon be canceled. In many of those cases, the insured have been offered new plans, often with better coverage but also at higher prices.