Barack Obama or rival Republican Mitt Romney to win without their support.
For Romney in particular, there are few paths to victory that don't pass through this Midwestern Rust Belt state.
Keenly aware of this, the Republican flew to Cleveland on Tuesday to rally volunteers for a final get-out-the-vote push at a campaign office.
Vice President Joe Biden made an appearance at a Greek diner in Cleveland, going booth by booth chatting up patrons, while Obama awaited the election results at home in Chicago.
One Ohio resident, Dave Rossi, said he dodged the flood of calls from pollsters and political groups that have bedeviled most Ohio voters because he uses an unlisted cell phone instead of a landline.
But the Republican still got the message: his vote mattered. That's the lesson he wanted his children to learn when he brought them to his polling place in the affluent Cleveland suburb of Highland Heights.
"I felt it inside that I needed to vote, more than I ever did," he said, after casting his ballot for Romney.
Sobhy Khalil, who also voted for Romney in Highland Heights, said he's glad the race is finally over.
"It was just tremendously irritating with the phone calls," he told AFP.
Khalil voted in mid-morning, when the pre-work rush had cleared out.
His polling place was busy but, unlike the mess of 2004 when voters had to wait hours to cast their ballots and many simply walked away, the lines moved quickly.
The 2004 debacle -- which saw President George W. Bush win a second term after less than 119,000 votes in Ohio gave him a narrow electoral college advantage -- led the Buckeye State to adopt flexible early voting rules.
Nearly 1.8 million people in Ohio voted early, which explains why there were so few lines observed Tuesday morning at several stations visited by AFP. But plenty of other people chose to participate in the Election Day ritual.
"It might sound kind of old-fashioned but I like voting on Election Day. I like going early. I want to make sure my vote gets there," Reggie Young said as he walked into a polling station in the University Heights neighborhood.
"Whoever wins Ohio gets into the White House, so it's very important for me to make this vote."
Young, who voted for Obama, said he and his friends discussed abortion and gay rights, but the economy was the main issue for them.
"This area was hit for a while. It looks like the jobs are coming back, but basically, it's the economy," Young told AFP.
Ohio's economy has been improving at a faster pace than the rest of the country, with its unemployment rate down to 7.0 percent in September compared with 7.8 percent nationally.
That's good news for Obama, who also benefits from his successful bailout of General Motors and Chrysler, given that one in eight Ohio jobs depends on the auto industry.
Print operator Tyrone Chisholm, 36, believes Obama has a lot more to offer the nation than just a firm hand on the economy.
"I understand him as a man, as a husband, as a father," he said. "It's not just one thing that he says. He really means a lot to this world."
At a polling place a few blocks away, Xamira Burgess said women's health issues galvanized her support for Obama.
"I feel like we have a right to say what we do with our own bodies, and no one has a right to say what we can and cannot do," she said.
Romney says he opposes abortion except in cases of rape, incest or a danger to the mother's health.
Ariel Travis, 18, was still trying to make up his mind as he walked into the polling station on Tuesday afternoon. He said he was leaning toward Obama because he prefers his stance on environmental issues.
"It was no easy choice for me," Travis told AFP.
"I really don't want to support either major party candidate because I think money has corrupted the political system. The reason I'm going to vote for Barack Obama is because Mitt Romney's plan for the environment is horrible."