FORTUNE — In a down-market strip mall 12 miles from the center of Columbus, Ohio, sandwiched between a Jackson Hewitt Tax Service and a “Check ‘n Go” payday lender, President Obama’s re-election effort has quietly planted a flag. It’s one of three field offices the campaign has opened in this crucial swing state to start selling a fragile claim: the economic recovery is real, and voters have Obama to thank for it.

Ohio went narrowly for Obama in 2008 but saw a dramatic Republican surge in 2010. Now, the president’s campaign is aiming to make its argument here by pointing to the president’s role in saving the American auto industry. His bet on taxpayer dollars to restructure Chrysler and General Motors (GM) looks to have paid off, and the rebirth of the car companies is helping the state’s turnaround outstrip the nation’s overall.

“This is a manufacturing state,” says Greg Schultz, the campaign’s state director, in an interview at a foldout table in the still-sleepy field office. “You know, we’re No. 2 in auto-assembly, No. 1 in auto parts. And the fact that there’s an unequivocal success in the auto loan, it provides a narrative that we can tell in all corners of the state.”

Schultz, a smiley 31-year-old with salt-and-pepper hair, grew up in the Cleveland area, the son of teachers. But his grandfather worked for GM, and he says most Ohioans are similarly removed by a single degree — if that. “People get it because they can see it,” he says. “There really is becoming an economic optimism. It’s not everywhere yet. But there are successes that people are starting to feel it.”

That incipient confidence is manifest nationally — a recent Wall Street Journal/NBC poll found 37% now believe the economy will improve over course of the year, up 7 points from just a month ago. And there may be no more politically consequential place for it to take root than bellwether Ohio, whose economy looks much like the national one, and which has gone for the presidential victor in every election since 1960.

Obama’s got a tough sell across the map. No president since Franklin Delano Roosevelt has been re-elected with unemployment above 7.2%, and the Federal Reserve projects the jobless rate to tick down only as low as 8.2% by the end of the year. So the re-election campaign is making a bet here that positive momentum will help carry the day, taking a cue from the President himself. Obama talked up the turnaround in his State of the Union address last week and emphasized the primacy of manufacturing jobs in his plan for accelerating it. He trumpeted the success of the auto bailouts as leading the way: “We bet on American workers. We bet on American ingenuity. And tonight, the American auto industry is back.”

Manufacturing is indeed playing a critical role in Ohio, providing one of every five new jobs in the state since the collapse, largely owing to car makers’ comeback, according to a report by Moody’s Analytics. Chrysler and General Motors have announced plans to invest a combined $560 million and add 1,000 new jobs in Toledo. Ford — which did not take government money during the downturn — is relocating production of two of its trucks from Mexicoto suburban Cleveland as part of a $128 million investment. With national car sales projected to jump by
1.5 million this year, Zachary Sears, a Moody’s Analytics economist, predicts “growth, but restrained growth” in the state.

The recovery aside, the Obama campaign believes it is heading into the election year with a major if unexpected tactical advantage in the Buckeye State. The decision by Ohio Republicans to push through a far-reaching package of reforms curbing collective bargaining rights for unions last year galvanized a moribund Democratic base. The party, working with an array of unions and other progressive groups, over the summer gathered signatures to force the issue to the ballot, then coordinated a $30 million effort to scrap the law. They won with 62% of the vote in what they have since described as a dry run for the presidential contest. “It’s allowed out organization to develop on the local level and the statewide level a coalition of progressive partners that we would not have been able to develop until months into 2012,” one campaign official says.

(Obama campaign manager Jim Messina, in a YouTube video explaining the campaign’s five likeliest paths to victory in November, says one runs through Ohio because it’s the state where Democrats have done “more work on the ground” than in any other in 2011.)

Republicans dismiss the assessment, pointing to another ballot measure that garnered even more votes by asking Ohioans to affirm their freedom to pick their own health care coverage. The GOP billed the measure as a rebuke of Obama’s health care overhaul, though its wording was vague enough to leave some question about whether voters understood it that way.

Either way, the Obama campaign is coming to life in Ohio. As Schultz discussed strategy, an older African-American man walked into the field office and shouted “Four more years!” to no one in particular. One of the office’s two full-time staffers materialized immediately, then sat him down to record his information. The campaign has plans to open more than 30 similar posts over the next two months, starting this week in Dayton, a hub for auto suppliers.

The plan is to eventually extend the campaign’s presence to all of the state’s 88 counties, including rural areas that are traditionally Republican strongholds. That approach was in evidence last November, when the campaign opened its second Ohio field office in Chillicothe, a small town in the Appalachian foothills. To understand why, consider the math. George W. Bush edged John Kerry in the state by fewer than 119,000 votes on his way to re-election in 2004. The Kerry campaign had focused on driving up its numbers in urban centers to the neglect of
the rest of the state. And it lost the southwestern counties of Butler, Clermont, and Warren by 132,000 votes alone.

Republican Gov. John Kasich, elected in the 2010 Republican sweep, is skeptical the Obama campaign’s strategy will bear fruit. “They’re not going to do well down there, I don’t care what they say,” he says. “There is a great energy in those areas to get the President out. It may not have that much to do with who the nominee is — they just want him out.”

But Kasich concedes this much: It will be close.