Under federal labor law, a union that bargains a contract for all employees can require employees who choose not be union members to pay fees to cover the cost of being represented, unless “prohibited by state or territorial law.” About half of the states have enacted such prohibitions, becoming right-to-work states.

Kentucky provides a perfect laboratory, said Jason M. Nemes, a Louisville lawyer involved in the initiative, because it is the lone Southern state that does not have a right-to-work law, and its neighbor West Virginia, where Republicans captured control of the Legislature last month, may soon pass one. Other states where Republicans expanded their control in the midterms, like New Mexico and Wisconsin, are also considering statewide bills.

A right-to-work law became a major issue in Kentucky’s midterm elections when Republicans, who control the State Senate, promised to pass one if they gained control of the House. They fell short of that goal, priming local officials like Judge-Executive Mike Buchanon, the elected head of Warren County, to act.

“We’ve always been interested in promoting right to work, and as all of our states around us became right to work, it has become a competitive issue,” Mr. Buchanon said, asserting that many businesses would not even consider locating in areas without right-to-work laws. He added that he was put in touch with Protect My Check by Senator Paul or one of his aides and was promised that the county’s legal bills would be covered.

Mr. Yessin, based in Tampa, Fla., said his group’s donors were not public but, other than his own contribution, all of the money raised so far had been from local businesses and employers in the targeted counties.

Last week’s vote in Bowling Green took local union members by surprise. It was advertised in advance as “an ordinance relating to the promotion of economic development and commerce,” and there was little public comment, though there were presentations by the Chamber of Commerce and the Bluegrass Institute, a policy group with close ties to ALEC.