On Thursday morning, the former Massachusetts governor held a rally for about 4,000 supporters in a factory called Jet Machine in Bond Hill. That’s in Hamilton County, the state’s third largest jurisdiction behind Cuyahoga and Franklin (where Columbus is located)…

Though Hamilton County is a bit smaller than the two Obama strongholds, it still boasts about 800,000 residents. That means Hamilton has a larger population than that of four states — Alaska, North Dakota, Vermont and Wyoming.

The demographics of the county mirror the state more closely than Cuyahoga does, although it is similarly home to a higher proportion of African-Americans, at about 25.8 percent. An Obama aide in Ohio told RCP this week, “We will win Hamilton County,” and returning it to the Democratic column could well be the difference if the election remains close.

In 2008, Obama won about 225,000 of the county’s votes compared with 196,000 for his opponent, a much slimmer difference than in Cuyahoga, of course. But two years later, Strickland lost Hamilton to Kasich in the governor’s race, 140,000 votes to 126,000. The voter registration stands at about 564,000.

Central to the Obama team’s thinking is that this is a presidential election, not a midterm, and they’ve built a stronger network of support since Strickland’s loss.