For both campaigns, the fight for Ohio amounts to a multi-front battle. The state’s industrial Northeast, especially Cleveland, is a Democratic stronghold. The rural counties in the south and west are solidly conservative. The auto industry dominates the northern tier of the state; the coal industry rules in the southeast.

In northern Ohio, the debate over the auto-industry rescue is seen by Obama forces as a gift. It is an issue where the two candidates have clear differences, with powerful local impact…

In southeastern Ohio, the Romney campaign is telling voters that Mr. Obama’s Environmental Protection Agency is hostile to the coal industry that some of them depend on. The Obama campaign has said that Mr. Romney, as governor of Massachusetts, tried to close a coal plant.

In other battlegrounds in the state, Mr. Jennings said the Romney campaign hopes to win back several key counties, such as Hamilton in the southwest and Lake in the northeast, that tipped Democratic in 2008 after previously being reliably Republican.