COLUMBUS, Ohio — A ballot battle in Ohio that pits the union rights of public workers against Republican efforts to shrink government and limit organized labor’s reach culminates Tuesday in a vote with political consequences from statehouses to Pennsylvania Avenue.

A question called Issue 2 asks voters to accept or reject a voluminous rewrite of Ohio’s collective bargaining law that GOP Gov. John Kasich signed in March, less than three months after his party regained power in the closely divided swing state.

Thousands descended on the Statehouse in protest of the legislation known as Senate Bill 5, prompting state officials at one point to lock the doors out of concern for lawmakers’ safety.

The legislation affects more than 350,000 police, firefighters, teachers, nurses and other government workers. It sets mandatory health care and pension limits for unionized government employees, bans public worker strikes, scraps binding arbitration and prohibits basing promotions solely on seniority.

By including police and firefighters, Ohio’s bill went further than Wisconsin’s, which was the first in a series of union-limiting measures plugged by Republican governors this year as they faced deep budget holes and a tea party movement fed up with government excess. Democratic governors, including New York’s Andrew Cuomo and Connecticut’s Dannel Malloy, have also faced down their public employee unions in attempts to rein in costs.

That’s why labor badly needs a win in Ohio, said Lee Adler, who teaches labor issues at Cornell University’s New York State School of Industrial and Labor Relations.

“If the governor of Ohio is able to hold the line on the legislation that was passed, then it would be a very significant setback for public sector workers and public sector unions in the U.S.,” he said.

“Likewise, if the other result happens, then it would certainly provide a considerable amount of hope that, with the proper kind of mobilization and the proper kind of targeting, some of the retrenchment that has been directed at public sector workers can be combated.”