COLUMBUS, Ohio  Republican state senators unveiled a new version of a bill governing public employee unions on Tuesday, saying it would preserve their right to collective bargaining, but Democratic lawmakers said the revisions failed to alter the essence of the bill, and in some cases made it even worse.

Most significant for local workers like police officers and firefighters was the change that would give elected officials the power to decide labor impasses, something that is currently handled by neutral third parties, said Mark Horton, the treasurer of the Ohio Association of Professional Firefighters.

“It’s worse than before,” he said. “We are beside ourselves.”

“This turns it totally political,” he added.

Republicans argued that the changes improved the bill, which is aimed, they said, at balancing the needs of public employees with those of cash-poor local governments. They said that a vote in the Senate on the bill could come as early as Wednesday.