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Dr. Aaron said businesses may resort to arguments about fairness or claim it violates the president’s promises to mask other motives. Some companies may have low-cost employees with an average age of 25 and fear the exchange — which, by law, limits the degree to which premiums can vary based on age and other factors — will hamper their economic edge since the exchange is designed to provide broad coverage, he said.

Council member David A. Catania, at-large independent and chairman of the Committee on Health, recently met with business owners “and had a very productive conversation about the exchange,” said Brendan Williams-Kief, the lawmaker’s spokesman.

“It’s important to note that there is still plenty of time and opportunity for public input and dialogue on how the exchange is set up,” he added.

Small businesses can stick with an existing insurance plan if they had it before the health care law passed in 2010, but they must work through the exchange if they switch their plans or make significant changes to them.

While critics say it will be difficult to maintain their grandfathered status, Dr. Akhter said the city is not looking to rock the boat. As the board members see it, the exchange will stabilize the insurance market and establish a transparent relationship between providers and consumers.

“If we disrupt the market place, it benefits no one,” he said, adding later, “Whenever there’s a change, there’s also fear and there are also concerns.”