There are two things Romney did that hurt him in Ohio. His opposition to the GM/Chrysler bail out, which directly or indirectly impacted about 20% of the population in Ohio hurt him. Even non-union competitors like Honda supported the bail out as the althernative would have devastated their supply chain. The second issue that hurt Romney was his opposition to mandatory coverage for birth control in the ACA. That was a two edged sword. Though very popular with Catholics in mostly rural western Ohio, he alienated a very large number of moderate to conservative, pro-business women in the State. Particularly suburban women in Cleveland, Columbus & Cincinnati metro areas.
The demographics in Ohio are really interesting. Rural Western Ohio is predominantly agricultural and Catholic and about 70% Republican. South east Ohio is culturally a part of Appalachia and again is about 70% Republican but only about 20% of the State live in these two regions. The Miami Valley Region (Cincinnati, Middletown and Dayton) have a very strong southern and appalachian influence and has typically speaking voted about 60% Republican in recent years. However, both of those regions are highly dependent on the automotive industry, so Obama's support of the auto bail out could be a game changer to a small degree. I say to a small degree because there are far, far to many hillbilly's in that region who would rather slit their own throats than vote for a niger. The Cleveland/Canton/Akron triangle is reliably democrat (about 60%) and is also the largest population center (40%). The region is more racially and culturally diverse than the Miami valley region and the auto bailout was very popular there in what is all ready a strongly democratic region so that will probably only have a small influence (though it certainly won't hurt Obama there). The real swing areas will be the Columbus and Toledo metro areas.
Columbus because it is by far the most diverse city in Ohio. Columbus is a manufacturing center, an education center, the center for State goverment, a regional financial center and it has a very strong corporate presense. The end result is a very diverse population Columbus metro area is the real swing region of the State. The Columbus city proper and the eastern suburbs is where most of the ethnic minorities (i.e. latinos and blacks) live and they are strongly democrat. The southern suburban area is mostly working class whites and are strongly Republican. The western and and northern suburbs are mostly middle and upper middle class and they are mostly independents with the business class usually voting Republican and the Professional classes usually voting Democrat and both capable of voting for either party based on who they think is the better person. So who ever wins Columbus will probably win the State.
Then there's the Toledo metro region. Half the morons there think they're in michigan so we don't pay to much attention to them.