It is unclear if the Health and Human Services Department has the legal authority to re-interpret the law’s definition of insurance plans that are “grandfathered” and could continue to exist, perhaps temporarily, under certain circumstances, even if those plans don’t meet the law’s basic benefits standards. The president has resisted suggestions on both sides of the aisle in Congress to extend the law’s open enrollment period beyond March 31.

Those who received cancellation notices from their insurance companies could choose another plan, or shop in the new exchanges, but their insurance will expire Dec. 31. To remain insured on Jan. 1, they would need to find and buy new coverage by Dec. 15.

When the ACA was written, advocates sought to limit the number of consumers who could retain insurance plans the government deemed substandard — plans sold by insurance companies to individuals who lacked the collective clout to bargain for better benefits at lower premiums and deductibles.

Obama said Thursday he wants to address, without legislation, what he now terms “a loophole” in his signature legislative achievement.