ELYRIA, Ohio >> The battle for Ohio is on, but for many voters here, choosing between President Barack Obama and Mitt Romney is like trying to decide between liver and brussels sprouts — a selection they would rather not have to make.

As it does every four years, Ohio is again unfolding as a crucial battleground in the presidential election, its 18 electoral votes critical to the equations of both candidates. Wednesday, Obama made his fourth trip to the state since January; Romney is expected to arrive Thursday, his first trip here since becoming the presumptive Republican nominee.

But putting together a winning strategy in Ohio will be a mighty challenge for both men, given that more than half of the state’s electorate — about 54 percent, according to the Brookings Institution — is white and working class, a group that both Obama and Romney have had a particularly hard time connecting with.

“Ohio is really ground zero for the white working-class voting bloc,” said William H. Frey, the senior demographer at Brookings. “That’s the key in Ohio.”

The sentiments of this group, loosely defined as whites without a four-year college degree in the middle and lower parts of the country’s earnings bracket, reflect feelings of economic uneasiness nationwide even as the overall economic picture in the country brightens. Many have not felt the effects of the modest recovery that has lifted the economy here in recent months, leaving them unenthusiastic about the president. At the same time, Romney is seen as awkward, unsympathetic and distant, a fundamentally uninspiring alternative.

Speaking of Obama, Patrick Cain, a utility company employee from nearby Brecksville, said: “There’s just no way I can vote for him. He talked about change, but has it been for the better? No.”

Yet Romney “comes from money and corporate America, a typical Republican,” said Cain, a registered independent. “I’m not going to say I like him.”

Elyria, a gritty city about 40 miles west of Cleveland where Obama spoke at a community college Wednesday afternoon, is dotted with scenes of industrial decline. Lorain County, which includes Elyria, has lost more than 11,000 jobs over the past decade, most in manufacturing.

“It’s hard being out of work, especially when you’re midcareer when you have to change jobs,” Obama told an audience of students from Lorain County Community College, some of them dislocated workers. “In this country, prosperity does not trickle down. It grows from the bottom up. It grows from a strong middle class out.”

Still, fresh signs of life in the automobile industry along with new jobs in the energy sector have lifted Ohio’s economy recently and pushed the unemployment rate down to 7.6 percent, lower than the national average. A Ford factory in the county has plans to produce a new line of trucks, and a steel plant, which was nearly dead, is now planning new production, with a boost from fresh purchases from the natural gas industry. Indeed, Ohio gained more jobs than any other state in February, said a spokesman for Gov. John Kasich, a Republican.

Economic improvement will be critical to Obama’s argument that he deserves re-election. But the economy is still considerably weaker than several years ago, many people are still unemployed, and Romney is likely to try to make those truths a central issue of the campaign.

“People don’t feel it,” said Sen. Rob Portman, an Ohio Republican who has been talked about as a potential vice presidential candidate for Romney. “There is still a lot of concern. Even folks who have jobs are nervous. People are not satisfied with the status quo.”

Obama carried Ohio by 4 percentage points four years ago, but his advisers concede that the state will most likely be even more competitive this time. For the past year, his campaign has been working to rebuild its statewide organization; it opened its 17th office this week. Obama’s struggles in Ohio have led his advisers to plot ways for him to win without it, like winning Florida or some combination of Virginia, North Carolina and Western states.

For Romney, winning without Ohio would be even harder, given that no Republican has ever taken the White House without it, and his campaign acknowledges that it is starting from behind organizationally. His narrow victory over Rick Santorum in the primary was a sign that he has work to do shoring up evangelical as well as working-class voters, although his supporters argue that his strength in the suburbs gives him a head start among swing voters like Cain who will decide the election.

“If this is a choice between Romney and the president, the president wins,” said former Gov. Ted Strickland, a Democrat who is national co-chairman of the Obama campaign and said he would travel across the state with a succinct message: “Osama bin Laden is dead, and General Motors is alive.”

But he conceded: “If the Romney folks are successful in diverting attention away from his positions and if the economy were to turn south, that would be an incredible challenge for the president.”

The issue of race still lurks. In two dozen interviews in Lorain County, four working-class people cited the fact that Obama was black as a reason they did not like him.

Obama is trying to broaden his appeal by pressing an argument of economic fairness and questioning whether a candidate steeped in wealth like Romney can understand people’s challenges.

“I wasn’t born with a silver spoon in my mouth,” Obama said in his speech at the community college. “Michelle wasn’t. But somebody gave us a chance.”

For some working-class voters, the case against Romney seemed to be working.

“He has a foreign bank account,” said Carol McMahon, a hotel receptionist and a registered independent who said she would vote for Obama. “That can’t be a good thing.”

But other voters were repelled. Kevin Gillespie, a medical equipment salesman who is a registered Democrat, said he believed Obama had presided over a drastic expansion of government, giving entitlements to the poor and forcing through a health care law that Gillespie did not like. His business has been booming since Obama was elected — he just bought a new Ford SUV — but he said that was not a reason to vote for the president.

“People say, ‘It’s going so well, what’s your beef?”’ Gillespie said. As for Romney, he said: “Do I want to vote for him? No.” Still, he said gloomily that Romney was “a consolation prize.”