A first-term senator with $3.5 million in the bank, Brown handily won election in 2006 but has seen his approval ratings plunge below 40 percent. He has amassed one of the most liberal voting records in the Senate, according to the National Journal’s ratings, a distinction he shares with several colleagues, including Harry Reid of Nevada, the majority leader, and Bernie Sanders, a self-described socialist from Vermont.

“It’s probably going to be a huge sticking point for a lot of Ohioans. On average, we’re a center-right state, and it’s all about appealing to that average voter,’’ said James Holland, a political science professor at the University of Akron.

Some independent voters, turned off by his liberal voting record, have already defected, polls suggest. But Brown remains confident.

“I get up everyday trying to fight for jobs. That’s my mission, and the election will take care of itself,’’ he told the Globe.

As Ohioans continue to grapple with a sluggish economy, the most significant threat to Brown is illustrated on the streets of Dayton.

Residents have witnessed the decay of this once-dynamic manufacturing hub. Downtown is quiet, home to rows of vacant buildings and storefronts displaying “space for lease’’ placards. The unemployment rate is 11.6 percent.

Dayton’s population has dropped nearly 15 percent in the last decade, and it has lost a lot of jobs as major businesses have either shut down or moved. In 2008, General Motors closed its sport utility vehicle assembly plant in nearby Moraine, leaving 2,500 workers without jobs.

“We’re watching the death of our city,’’ said Tammy Minehart, 40, a registered nurse at Good Samaritan Hospital.

Minehart has voted for Democrats her entire life, including Brown in 2006. But she has grown disenchanted with a party that she says is “too focused on playing politics’’ as her hometown continues to crumble. It has swayed her to consider shedding an allegiance.