As the Supreme Court hears arguments on Wednesday in the latest challenge to the Affordable Care Act, health insurers are struggling to prepare for a decision that could unravel the marketplaces created by the law.

The ruling could come in June—but insurers must make regulatory filings before then about their 2016 plans. Utah’s Arches Health Plan, for one, says it may propose an array of insurance product designs this spring. Then, depending on what the court decides, the insurer would be poised to drop some of them before...