Insurers emphasized that the new insurance markets would need to have a balanced mix of people, including the young and healthy. They and White House officials discussed ways to address the insurers’ concerns that the balance would be disrupted if more people than expected kept their old coverage throughout the year as well.

The White House acknowledged that making the changes the president was suggesting would be challenging. “We believe that insurers certainly can generate letters, just like they did already, to their customers that advise them of this new opportunity if they choose to make that opportunity available to them, and if there is time to do that,” said the White House spokesman, Jay Carney. “So we’re obviously going to be working with insurers and working with states on this matter. But we believe there is time, and we believe it’s a solution to a problem that has clearly arisen that the president wants addressed.”

Even if the insurance industry and the president find common ground, thousands of consumers may still not be able to renew their old policies.

Insurance policies are typically policed by the states, which will have a powerful voice in how all of this is resolved.

Already, some states, including Washington and Arkansas, have said they will not allow insurers to extend policies that do not comply with the guidelines established by the minimum standards set by the Affordable Care Act. Rhode Island also announced on Friday that it would not go along. “After reviewing the president’s announcement, we have decided to continue in the direction we are going and therefore will not be adopting the option made available to us by the president,” state officials said.

Some other states, notably Florida, are going to allow renewals. In New York, officials were hashing out a plan on Friday to deal with the change in policy, and an announcement could come early next week.

Logan Harrison, chief deputy commissioner of the Indiana Department of Insurance, said his state had not decided how to proceed but the fact that they were having to scramble to do anything was maddening.