Two prominent polls of the state last month showed the presidential race in a statistical tie. Turnout in the Ohio primary elections in April was higher for Democrats than Republicans for the first time in a dozen years, evidence of enthusiasm in the Democratic base. And the Trump campaign recently booked $18.4 million in fall TV ads in Ohio, more than in any state besides Florida — a sign that Mr. Trump is on the defensive in a state that until recently seemed locked down for Republicans.

With Democratic leaders urging Mr. Biden, the presumptive nominee, to expand his ambitions to states previously considered out of reach, Ohio offers Democrats the possibility of seizing on suburban gains they have made in the Trump era, while restoring parts of the old Obama coalition.

“The definition of Trump being in trouble is that he’s forced to spend $18 million on TV in Ohio and he’s mired in a battle for his life here,” said David Pepper, the chairman of the Ohio Democratic Party…

For all the optimism of Democrats, though, the Buckeye State just might be an illusion in the mists. Not only did Mr. Trump win handily in 2016 — by eight percentage points — but Democrats also fell short in the 2018 midterm elections in Ohio compared with their gains in the “blue wall” states of Wisconsin, Michigan and Pennsylvania.