The City Council is set to override a mayoral veto on an amended measure to force large grocery stores to dig deeper into their pockets for employee health benefits.

Aimed at stores like Wal-Mart, the Health Care Security Act requires employers of large grocers to match the average rate of health coverage contributions that other grocers pay in the city, which could mean an expenditure of $2.50 to $3 an hour for each employee.

The City Council first passed the bill last year, but lawmakers quickly drafted an amendment after some mid-sized stores said they would face crippling costs as a result.

Acknowledging that the bill’s target was “big box” and warehouse club stores, council members agreed to raise the minimum size – in space and number of employees – of stores that would have to comply with the measure. Mayor Bloomberg vetoed both the original bill and the amendment, and the law was seen by many as an attempt to block Wal-Mart from opening a store in the city.

Supporters of the bill say it could reduce the number of uninsured workers, while opponents contend the higher health care costs could drive large businesses out of the city.

The law could still face a legal challenge from the Bloomberg administration.