Reinstating canceled policies would be a scramble for insurance companies, whose coverage plans need to be approved by state regulators — a process that can take months…

If millions more people can suddenly invoke the grandfather clause, said one analyst, that would change the assumptions insurers made when they calculated the premiums they are now offering in the marketplace.

Many of those who want to keep their plans pay very low-cost premiums because they aren’t sick and don’t use the healthcare system much. Those are exactly the participants the insurers are counting on joining the new insurance pools to help pay the freight for everyone else.

“If those people don’t come into the pool next year, then the premiums the insurers bid for the 2014 policies might be wrong,” said Gary Claxton, a vice president of the Kaiser Family Foundation.

If millions of people who have coverage now can keep it as long as they wish without complying with new rules, Claxton said, the healthiest of them will probably choose to do so — until they get sick and decide to cash in on the benefits of the new marketplace.