BEXLEY, Ohio -- President Barack Obama pushed a new message in the fight for the presidency Tuesday, touting his administration's efforts to make college more affordable and contrasting them with opponent Mitt Romney's proposed cuts to higher education funding.

Speaking before a receptive crowd of 3,300, including many college students, on the suburban Columbus campus of Capital University on a sun-splashed afternoon, the Democrat emphasized his commitment to help cut college costs with federal grant and loan programs like the ones he used to pay for school.

"I am only standing before you today because of the chance my education gave me," Obama said. "So I can tell you with some experience that making higher education more affordable for our young people is something I've got a personal stake in. It's something I've made a top priority of my presidency. And in Ohio, it's something that is very much at stake in this election."

With just six weeks until early voting begins in Ohio, Obama made his 10th trip to the state this year, focusing his pitch on his efforts to make higher education more accessible. He took credit for 3 million more students who received federal grants than under previous administrations.

Romney's camp quickly fired back, blaming the rising costs of a college education on what they called Obama's failed economic policies.

Obama's speech was part of a two-day education-focused trip to Ohio and Nevada -- a pair of the handful of swing states that will make or break his quest for a second term.

Telling the debt-strapped students in the crowd, "I've been in your shoes," Obama paraphrased remarks his Republican opponent had made recently in Ohio to draw a sharp contrast.

"A few months ago, just up the road in Westerville, Gov. Romney said if you want to be successful, if you want to go to college or start a business, you can just 'borrow money if you have to from your parents,'" Obama said.

And in Youngstown, the former Massachusetts governor advised a high school student who asked about the high cost of college that "the best thing I can do for you is to tell you to shop around," Obama said. "That's it – that's his plan," Obama said. "That's his answer for a young person hoping to go to college – shop around, borrow money from your parents."

Obama sought to tie Romney's comments to a budget proposal from his vice presidential candidate, Rep. Paul Ryan, that would cut federal student aid as part of a plan to help pay for more extensive tax cuts.

"It's a vision that says we can't help young people make it because we need to protect those who have already made it," Obama said.

The Romney campaign, noting that Obama was back in Ohio for the second time in three weeks, referred to the president as "the Campaigner-in-Chief" and said Obama was to blame for higher college costs.

"Under President Obama the costs of college in Ohio have skyrocketed, making it more difficult for students to attend college; and his economic policies have made it harder for graduates to get jobs," said Christopher Maloney, Romney for President spokesman. "Mitt Romney and Paul Ryan have a Plan for a Stronger Middle Class to get our economy back on track and ensure that young Americans have the skills they need to compete in a competitive global economy."

College affordability is a potent issue for many middle-class Ohio families feeling the sheepskin squeeze. The Buckeye State is one of the more expensive states for residents to go to college, with in-state tuition costs averaging $18,190 last year.

Before his speech, Obama made an unscheduled stop at a larger university, Ohio State, where he chatted up students at Sloopy's Diner in the Student Union.