Disputes between unions and employers over paying for new costs associated with the Affordable Care Act are roiling labor talks nationwide.

Unions and employers are tussling over who will pick up the tab for new mandates, such as coverage for dependent children to age 26, as well as future costs, such as a tax on premium health plans starting in 2018. The question is poised to become a significant point of tension as tens of thousands of labor contracts covering millions of workers expire in the next several years, with ACA-related...