Employer groups and insurers are pushing to keep businesses with 51 to 100 workers exempt from a provision of the federal health law that they say could significantly increase their costs.

For these midsize employers, the Affordable Care Act’s requirements for what health plans must cover—and how they are priced—are set to take effect on Jan. 1, 2016.

Already the law requires insurers to sell individual and “small group” plans to everyone at the same price, regardless of their health. Those rules, which kicked in Jan 1, 2014 for businesses with 50 or fewer workers, also set standards for what health-benefits packages must cover.