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“It’s very frustrating to be in a situation where, quite frankly, the problems were exacerbated by the fumbles of the [Obama] administration in getting out the program of,” he said.

In Washington — one of the 15 states that embraced the health care reform and set up their own exchanges — Insurance Commissioner Mike Kreidler said insurers would not be able to renew plans that flout Obamacare. He said such a move might destabilize the state-run health care exchange, which is working relatively well, by allowing young, healthy people to stay on low-level plans instead of enrolling in the Obamacare market.

Kentucky’s insurance commissioner, Sharon P. Clark, said Monday that she doesn’t fear tumult in her state’s individual market over Mr. Obama’s plan, even though her state also boasts a high-performing exchange.

Like Florida, her state allowed insurers to extend plans into 2014 instead of risking cancellation under Obamacare. She said other states might be having difficulties “because they might not have had the allowance for early renewal.”

California Insurance Commissioner Dave Jones is encouraging insurers to let residents keep their health plans in the coming year. He said roughly 1 million residents with canceled plans should have the freedom to renew their plans in line with Mr. Obama’s original promise or shop for alternative plans on Covered California, the state’s exchange.

While he awaits feedback from insurers, he has found some cancellation notices that include errors, effectively allowing some customers to keep their existing coverage until the end of March.

He does not think the proposed renewals will cause tumult in the state exchange’s stability, since there are safeguards within the law to deal with adverse changes to the risk pool. Additionally, estimates show that up to 400,000 Californians could be eligible for subsidies to defray their premiums, making the exchange more attractive.

“These concerns about impacts on the exchange are extraordinarily misplaced People are very price-sensitive. We’re encouraging people to shop,” he said.

Officials in Tennessee and other states are trying to understand the long-range impact of Mr. Obama’s proposal and haven’t decided one way or the other.

“The governor and commissioner’s primary goal is to maximize Tennesseans’ options in the evolving health insurance marketplace,” said Alexia Poe, spokeswoman for Gov. Bill Haslam, a Republican. “They also believe that Tennesseans should be able to keep the coverage they were assured they’d be able to keep.”

Dave Boyer contributed to this report.