Health insurers that lost millions of dollars last year under the Affordable Care Act may wait years for the government to deliver the aid it promised them.

Companies, including Downtown-based insurer Highmark, want about $2.87 billion to help cover their first-year losses from online insurance marketplaces — a centerpiece of the landmark health care law. But a federal relief program meant to limit their risk is more than $2 billion short, leaving the companies to collect only 12.6 percent of those requests late this year, the Centers for Medicare & Medicaid Services said this month.