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While polls show Mr. Obama leading slightly in Pennsylvania and Ohio, both campaigns are making these states priorities.

Mr. Obama formally launched his campaign here and returned to Cleveland last week for a high-profile economic speech that his campaign cast as a chance to stem the flow of bad news that followed the most recent jobs report, which showed that the national unemployment rate ticked up to 8.2 percent.

History suggests that Ohio is a must-win for Mr. Romney: No Republican ever has won the presidency without winning the Buckeye State.

George W. Bush won the state in 2000 and 2004, defeating Al Gore and John Kerry of Massachusetts, respectively. Mr. Obama turned the tide here by winning the state in 2008.

The political dynamic, though, is further complicated by the state’s unemployment rate having dropped consistently over the past year. Last year, Democrats showed their political muscle by passing a referendum that reversed a law backed by Mr. Romney that would have curtailed collective-bargaining rights for 360,000 public employees.

Mr. Romney has some heavier lifting to do in Pennsylvania, where no Republican presidential hopeful has won since George H.W. Bush captured it in 1988. Observers, though, say the political environment has shifted dramatically during the first term of the Obama administration.

Stuart Stevens, a top Romney adviser, said the election will be a referendum on Mr. Obama’s handling of the economy and that his boss has an opportunity to make inroads with more middle-class voters who have fallen on tough times.

“Every re-election is an MRI of the president’s record, and it is hard to find anybody who voted for McCain who is planning to vote for Obama, and there is a very large group of people out there who voted for Obama who are open to voting for Mitt Romney,” he said.

Asked to handicap the race, Jim Schick, of Conneaut, Ohio, predicted that Mr. Romney will win his state because young voters are not as excited as they were about Mr. Obama in 2008 and because the economy has put many middle-class and independent-minded voters up for grabs.

“I think it is going to be those four or five more unemployment reports that come out, and I think that is going to be the biggest thing in this election,” the 52-year-old said.