In Ohio, joblessness was 9.1 percent in February 2009, shortly after Obama took office. It stood at 7.6 last month.
In North Carolina, joblessness was 9.5 percent then, and stands at 9.9 now.
In Michigan, where Obama was appearing late Wednesday, it was 12.5 percent in 2009 and is 8.8 percent now.
In all three states, unemployment rose in the months immediately after Obama took office as the recession deepened and financial markets trembled.
"Right now we have two competing visions of our future. And the choice could not be clearer," said Obama. He said he was sure Republicans were "patriots. I'm sure they're sincere in -- in terms of what they say. But their theory, I believe, is wrong."
Without mentioning Romney by name, he said, "Instead of moderating their views even slightly, you now have Republicans in Washington, the ones running for president, proposing budgets that shower the wealthiest Americans with even more tax cuts, folks like me who don't need them, weren't looking for them."
But Romney was relentless as he ripped into the president.
"Virtually nothing he has done has made it more likely for people to get jobs," he said.
Reading from Obama's campaign pledges from the 2008 Democratic convention in Denver, he said the president has "failed by the measurements he set. You won't hear that at this convention, but you're going to hear it at ours."
He added: "We're a trusting people. We're a hopeful people. But we are not dumb, and we are not going to fall for the same lines from the same person just because it's a different place."
Nancy Benac reported from Elyria, Ohio. Associated Press writer Stacy Anderson contributed from Washington.
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