Groups call for levies on firms that fall short on health-insurance

The non-profit sector, too, is concerned with Baker's proposal. Most non-profits offer good health coverage to their employees, Massachusetts Nonprofit Network CEO Jim Klocke said, but would still be penalized if workers elect to either stay on their parents' plan or take coverage through a spouse's plan.

"Most non-profits run on very tight budgets, so any time you have an unexpected expense -- and this is a high level of assessment, $2,000 per employee -- the result of that for most non-profits would be service cuts or layoffs," Klocke said. "There is no wiggle room in their budgets to handle it."