Obama, who spoke in politically pivotal Ohio, said Republicans "don't seem to remember how America was built."
Pounding home the theme of his re-election run, Obama said the rich should pay higher taxes to support priorities, such as education, that help the entire nation.
"In this country, prosperity doesn't trickle down," Obama told an audience of roughly 400 people at Lorain County Community College. "Prosperity grows from the bottom up and it grows from a strong middle class out."
"That's why I'm always confused when we keep having the same argument with folks who don't seem to remember how America was built," Obama said.
In Charlotte, N.C., Romney gave a scathing indictment of Obama's policies. The Republican presidential nominee-in-waiting said virtually nothing Obama has done in his time in the Oval Office has helped create jobs.
Romney said more Americans have lost jobs, more houses have plunged in value, gasoline prices have doubled and health care costs have risen during Obama's tenure.
Romney spoke Wednesday across the street from the Bank of America Stadium, where Obama will accept the Democratic Party's nomination to a second term in early September.
Obama did not call out Romney by name.
"We have two competing visions of our future," Obama said. "The choice could not be clearer. Those folks running on the other side, I'm sure they are patriots, I'm sure they are sincere in terms of what they say, but their theory, I believe, is wrong."
Each candidate has material to work with in making his economic case: Nationally, the unemployment rate has dropped from 9.1 percent last August to 8.2 percent in March, the lowest since about the time Obama took office. But job growth has been weak, millions of people remain unemployed and improvements in hiring haven't translated into higher salaries for those who are working.