President Obama made an impassioned appeal Tuesday to the types of young people who powered his campaign four years ago, pledging to keep college affordable and mocking rival Mitt Romney’s commitment to federal student loan programs.

At an outdoor rally at Capital University here, Obama told a crowd of 3,300 that he and his wife Michelle understand firsthand the burden of a “mountain of debt” from loans because when they married after law school they “got poor together. We combined our liabilities into one big liability.”

The president contrasted that with Romney, whom he lampooned for telling college students in April to “borrow money from your parents” to get through school.

“I want to make sure everybody understands not everybody has parents who have the money to lend,” Obama said. “You know, that may be news to some folks, but it’s the truth.”

In a 25-minute speech, Obama attacked the presumptive GOP nominee’s budget plans, which the president said would slash education spending by 20 percent, jeopardizing 1 million students’ Pell Grants over the next decade.

With student loan debt having surpassed credit card debt, Obama has attempted to ease the burden on students and graduates, announcing a series of smaller-scale initiatives during stops on college campuses over the past year. In June, Congress approved a plan to extend by a year low-interest rates on some federal student loans, a move Obama pushed for in several speeches.

The moves also are aimed at appealing to the cohort of young voters that helped propel Obama’s candidacy four years ago, but which has soured somewhat in a sluggish economy that has made it difficult for many to find jobs. Obama has pushed for additional investments in education, infrastructure and other programs to help spark growth, while Republicans have criticized him for spending too much at a time when the federal debt has continued to soar and unemployment remains at 8.3 percent.

The education offensive came after Obama had spent a week attacking Romney, and his vice presidential running mate Rep. Paul Ryan (Wis.), on topics such as Medicare and taxes. The Romney campaign responded Tuesday by arguing that college costs have “skyrocketed” under Obama, making it more difficult for students to gain access to higher education.

Furthermore, “his economic policies have made it harder for graduates to get jobs,” Romney spokeswoman Amanda Henneberg said in a statement.

The trip to Ohio, a crucial swing state, was Obama’s 10th this year, according to the campaign. He was scheduled to fly to Reno, Nev., on Tuesday afternoon to deliver a similar message on student debt and education at a community college. He will appear in Las Vegas on Wednesday, then attend a series of fundraisers in New York City, before returning to Washington.

Before arriving at Capital University, Obama made an unannounced stop at Ohio State University, also in Columbus, where he ducked into Sloopy’s, the student center, and ordered a lunch of a classic Reuben, potato chips and a Buckeye Pie made of peanut butter, chocolate and whipped cream.

Then he posed for pictures with students, and even used his arm as the “I” when a group spelled out O-H-I-O.

“The only problem seeing you guys,” he told one group of young women, was that his daughter, Malia, was starting high school this year and would be moving out in a few years to go to college herself.

One of the students, Samantha Williams, of Lima, Ohio, asked, “Are you ready?”

“No,” Obama replied, “I don’t want them to leave yet.”

During his remarks at Capital University, Obama also mentioned Malia and his younger daughter Sasha while emphasizing how important it is for young people to be able to go to college.

Toward the end of his speech, the president called on students to register to vote and rally their friends.

His Republican rivals, Obama told the crowd, are “counting on young people sitting this one out. They say, well, you know what? Obama — he’s grayer now, he’s not as new and as fresh as he was in 2008, so young people aren’t going to turn out the same way. . . . Let’s prove the cynics wrong. Let’s show them your vote counts.”