“As a pragmatic matter,” said a White House official, “it will be up to insurance commissioners and states.”

Insurers and regulators worry that under the new proposal, too many people will continue their old plans. These policies are likely to be less expensive than coverage in the exchanges because the benefits are not as great and they were sold to a generally healthier group. Insurers priced their policies for 2014 based on the assumption that everybody would have to be in the new market, and they and regulators worry that their costs will be much higher if only older and sicker people enroll in the new plans.

Health insurers also said the result could be much higher costs — and therefore higher prices for consumers — than expected.

“Changing the rules after health plans have already met the requirements of the law could destabilize the market and result in higher premiums for consumers,” said Karen Ignagni, the president of America’s Health Insurance Plans, a trade group in Washington.

In California, another state with a well-functioning marketplace, health plan officials also expressed opposition to the idea. “Reversing course now could cause a significant disruption in the marketplace,” said Patrick Johnston, the chief executive of the California Association of Health Plans. “The entire underlying premise of the A.C.A. — balancing costs of the young, old, sick and healthy — has been left adrift with this announcement.”

Amid the outcry, a few regulators expressed some support for the idea while others withheld comment until they had more time to digest it.

California’s insurance commissioner, Dave Jones, said he had already forced two companies, Blue Shield of California and Anthem Blue Cross, to delay the cancellation of policies for about 220,000 customers for a few months to allow them more time. His support for the president’s proposal could put him at odds with the officials running the state marketplace who want as many people as possible to enroll in one of the new plans.