Workers at U.S. assembly plants for General Motors Co. and Ford Motor Co. are likely to get 2014 bonuses exceeding $6,000 each, capping a four-year labor contract under which profit-sharing checks have gone to factory employees in record amounts. But the United Auto Workers union, gearing up for negotiations with Detroit’s Big Three next summer, is prepared to argue that isn’t good enough.

After 10 years without hourly wage increases as well as an agreement by the union to accept lower pay for new hires, compensation is increasingly...