The Senate gave the bill tentative approval on a 23-19 vote Thursday before starting debate on the $5.7 billion state budget because it affects that spending plan.
Local governments say losing the money would cut into police, fire and ambulance services.
Senate Finance Committee Chairman Hugh Leatherman of Florence says there is no way to help local governments without making deeper cuts in state spending. He says that could mean closing some agencies.
Leatherman says local governments have been spared the midyear budget cuts in state funding that have taken nearly a quarter of the state spending at most state agencies.