Just 10 days after wrapping up a bus tour of Ohio, President Obama returned to this crucial swing state Monday for a town hall in a heavily Republican area.

At Cincinnati’s Music Hall, where he also held a fundraiser, Obama continued to make appeals to the middle class by emphasizing his administration’s bailout of the U.S. auto industry and his proposal to extend the George W. Bush-era tax cuts for the middle class.

The president also kept up his attacks on Republican rival Mitt Romney by suggesting that the former Massachusetts governor supports limited taxing of U.S. corporations abroad that would encourage more jobs to flow overseas.

“We have not found a serious economic study that says Gov. Romney’s economic plan would actually create jobs, until today, I have to be honest,” Obama said, citing a Tax Notes report. “Today we found out there is a new study by non-partisan economists that says Gov. Romney’s economic plan would in fact create 800,000 jobs. There’s only one problem. The jobs wouldn’t be in America. . . . We don’t need a president who plans to ship more jobs overseas.”

Obama has proposed offering tax breaks to U.S. companies that bring jobs back to the United States.

The Obama campaign has put special emphasis on Ohio, which has emerged as a bellwether state whose voters have supported the winner in the past 10 presidential elections. Obama formally kicked off his reelection effort with a speech in Columbus in early May, and he delivered a lengthy economic address in Cleveland in June.

Though both sides believe the race will be tight, polls show Obama holding a small but steady advantage in Ohio and other swing states. His campaign has outspent Romney by $91 million to $23 million on television ads in those battlegrounds. Obama’s ads largely criticize Romney’s record as the former head of Bain Capital, a private equity firm that has come under scrutiny for investing in companies that helped send U.S. jobs offshore.

The Romney campaign, which is facing increased criticism from Republicans about its strategy, sent out a memo Monday morning that suggested that the attacks on Romney’s record were in fact falling flat and not moving the needle in terms of polling.

“President Obama’s campaign will never have a more substantial advertising advantage than it has had over the past few weeks, yet there is no evidence to suggest that the ballot has moved,” wrote Neil Newhouse, Romney’s pollster. “If throwing the kitchen sink at Gov. Romney while leveraging a two-to-one ad-spending advantage doesn’t move numbers for the President, that’s got to tell you something about the state of the electorate: Voters are frustrated with President Obama’s failure to keep his promises from the 2008 campaign and don’t truly believe the next four years will be any different from the last three and a half.”

Romney has defended his record, saying Bain created jobs during his tenure and that the firm invested in companies that helped outsource jobs only after Romney gave up day-to-day management in 1999, when he left to organize the winter Olympics in Utah.

Speaking at a fundraiser in Baton Rouge, Romney defended his record to supporters.

“I’m not going to apologize for being a successful businessman,” Romney said. “Those who take risks sometimes succeed brilliantly, wonderfully and that makes us a stronger economy.”

But the Obama campaign has seized on news reports that Bain continued to list Romney as its chief executive three years later in filings to the Securities and Exchange Commission.

That debate, which dominated the campaign news cycle last week, has put Romney on the defensive, and the GOP candidate failed to put the matter to rest even after conducting a series of five network television interviews Friday.

“Romney has been unable to explain how he accepts no responsibility for what happened at Bain after February 1999 while remaining CEO, President, and Chairman of the company,” Obama campaign spokesman Ben LaBolt wrote in a memo distributed to reporters on Monday.

Appearing on MSNBC’s “The Daily Rundown” program on Monday, Romney spokeswoman Gail Gitcho blasted the Obama campaign for creating distractions to more substantive issues, such as the 8.2 national unemployment rate.

“They want to talk about anything but their failed record on the economy,” she said.

The Romney campaign, meanwhile, rolled out a new offensive Monday, accusing Obama of “crony capitalism,” a theme that Romney has touched on throughout his campaign but has yet to hammer consistently.

The overall effort, under the branding “Obama’s Political Payoffs and Middle Class Layoffs,” will highlight alleged administration favoritism toward more than 200 Obama donors. Romney is expected to push this line of attack Tuesday at a campaign event in Irwin, Pa., but he previewed it Monday in Baton Rouge.

“When the president puts $500 million into a company called Fisker whose owner happens to be a venture capital firm in which Al Gore is a partner, that stinks. It doesn’t look right. It doesn’t smell right, and that has happened more than once,” Romney said. “And then there’s something else which gives us trouble, and that is he took that half a billion and put it in Fisker, and then they outsourced the jobs to manufacture that car in Finland. So the president not only took our money and put it with his friends — he also took our money and outsourced the jobs, so I’m referring to him as the outsourcer-in-chief.”

Aides for Obama suggested that Romney was trying to “change the conversation because he doesn’t want to answer questions about his time at Bain Capital.”

“President Obama has set a bar of transparency that Mitt Romney has not met, cannot possibly meet, even on his tippy-toes,” said Jen Psaki, Obama’s traveling press secretary. “We have released bundlers, we release people regularly who visit the White House. We release far more than Mitt Romney has come close to. These are old, tired, haggard attacks.”

Romney will return to Ohio for campaign events on Wednesday.