While he and presumptive Republican presidential nominee Mitt Romney have "many disagreements" about how to lead the country, Obama said there was one issue "in which I stand in complete agreement with my opponent."
"This election is about our economy future," Obama said.
In Cleveland, meanwhile, Romney said Obama has failed to deliver on his promise to improve the economy.
Obama, Romney said, has made it harder for businesses to "create more jobs."
He challenged Obama to visit large and small employers and ask whether his policies helped put people back to work, noting that the nationwide jobless rate has been above 8 percent for 40 straight months.
While on the stump, Romney said business owners told him the administration's policies "make it harder for them to put people back to work" and that they feel "this administration sees them as the enemy."
"So as you look at the president's record, it is long on words and short on action that created jobs," Romney said. "And, again, talk is cheap. Action speaks loudly. Look what's happened across this country."
"If you think things are going swimmingly, if you think the president's right when he said the private sector is doing fine, well, then he's the guy to vote for," Romney said.
Obama told the 1,500 people at Cuyahoga Community College the election "presents a choice about two fundamentally [opposite] visions" about how to sustain economic growth, pay down the national debt and generate good jobs for the middle class.
"The decisions we make … will have an enormous impact on this country and the country we pass on to our children," he said.
"What's holding us back is a stalemate in Washington about two fundamentally different views about which direction America should take," he said. "This election is your chance to break that stalemate. At stake is not simply choice between two candidates or political parties, but two paths for our country."
Romney and his Republican allies want to reinstate the theory that economic prosperity will flow from the top down that was tried before he took office, Obama said.
"How did this economic theory work out?" Obama asked.
Financial institutions and big corporations saw their profits soar, Obama said, but "the prosperity didn't trickle down to the middle class."
Those who believe these policies work, Obama said, should vote for Romney.
"I understand if you agree with the approach I just described," he said. "If you want to give the policies of last decade another try, vote for Mr. Romney."
"I believe their approach is wrong," Obama said to applause and cheers. "And I'm not alone."
He cited a Moody's analysis that indicated the Republican plan "would do more harm in the short term … push us deeper into recession and make this recovery slower."
"We can't afford to jeopardize [the] future [of America] by repeating the mistakes of the past," Obama said. "I've got a different vision for America."
The federal government can't reduce its debt "without a strong and growing economy and we can't have a strong and growing economy without a strong and growing middle class."
He restated his platform for building a strong economy that includes investments in education, green technology and research and development, revamping the tax code, producing energy domestically and "everybody paying their fair share."
Republicans may be offering a plan "to win the election, but it is not a plan to create jobs, grow the economy [and] pay down the debt … and it sure is not a plan to revive the middle class and our future," Obama said, "I think you deserve better than that."
"If you believe the economy grows best when everybody gets their fair shot ... and plays by the same rules," Obama said, "I ask you to stand with me for a second term as president."
In a pre-speech rebuttal, House Speaker John Boehner released a video Thursday suggesting Obama could help revive the economy by pushing the Democratic-controlled Senate to vote on House Republican-sponsored legislation, The Washington Post said.
Boehner said the economy- and jobs-related bills passed in recent weeks by the Republican-led House "aren't big, controversial bills that no one has read -- they're practical, common-sense proposals to help small businesses create jobs and build a stronger economy for all Americans."
Boehner aides told the Post the legislation seen on his desk in the video includes bills that would reduce taxes for small businesses, control or repeal some federal regulations and repeal the healthcare reform law. None of them likely will be brought to a vote in the Senate.
The Republican National Committee also created a video pre-emptively responding to Obama's "economic framing speech."
The video asserts Obama pretends to focus on creating jobs, when he is actually doing the opposite.
"Even though he claimed to be focused on jobs, Obama instead spent his time making it harder for job creators by passing Obamacare, more regulation and pushing for higher taxes," the committee said in a statement.