But Haislamier said, "This is going to be a fix in controlling costs and disruption in the market, which is something that the Obama administration had been willing to tolerate as the cost of expanding the market." He had been involved in drafting proposals for the rule while working for the Trump health-care transition team until two weeks ago.
Haislmaier said suggestions for the proposed rule had included limiting the number of special enrollment periods during which people can sign up for insurance plans outside of the narrow open-enrollment season, and tightening eligibility verification standards for special enrollment.
Haislmaier also said the rule could include a requirement that people whose insurance premiums are in arrears settle those debts before signing up for a new plan.
However, a person who was informed about the new rule told CNBC that there appeared to be neither a decrease in the number of special enrollment periods, nor a provision of requiring people to settle their past-due premiums before a new enrollment.
That source said that they believed the new rule would require documentation proving eligibility for a special enrollment from 100 percent of customers, as opposed to just 50 percent of customers.
People who buy Obamacare plans normally can sign up for coverage only during open enrollment, which for 2017 ran from November 2016 through Jan. 31. People who don't sign up during that time are normally barred from enrolling in coverage until next November, when 2018 enrollment begins.
However, the law allows exceptions for people who experience certain life events — including marriage, divorce, birth of a child, loss of health coverage and moving one's residence. In past years, the Obama administration also allowed special enrollment periods for people who were confused about when to sign up, or who had to pay an Obamacare fine in 2015.
Haislmaier said that the possible changes, which would go further than recent efforts by the Obama administration to tighten up rules around special enrollments, could make a substantive difference for insurers, "in the aggregate." Some insurers would benefit more from the moves than others, he said.
Haislmaier said controlling costs and disruption in the individual insurance market is "part of the political impetus of the Trump administration agenda of 'repeal-and-replace' " Obamacare.
And if fewer people end up being enrolled in Obamacare plans as a result of the proposed rule, the administration "can live with that," he said.
While the Trump administration pursues its strategy of repealing and replacing Obamacare, Haislmaier said, insurers have to file their proposed rates for individual plans for 2018 by this spring. The new rule would help alleviate some insurers' concerns about their costs as they prepare those rates, he said.