Obama traveled to Ohio State University to make his point the day before classes were due to start.
"Your education is the single most important investment that you can make in your future," Obama told cheering students.
"The degree that you earn from this university is the surest path that you will have to a good job and to higher earnings. It's the best tool you'll have to achieve what is the core promise of this country -- the idea that if you work hard, your work will be rewarded."
Obama said the budget plan supported by presumptive Republican presidential nominee Mitt Romney would cut government grant programs so deeply "that 1 million of those students who we have helped would no longer get a scholarship at all."
Obama said we cannot allow the economic hardship wrought by the recession prevent young Americans from getting an education.
"Think about all the discoveries, all the businesses, all the breakthroughs that we would not have made if we told every young person who has got the drive and the will and the grades to go to college, 'Tough luck, too bad, you're on your own,'" Obama said. "We've always made a commitment to put a good education within the reach of everybody who is willing to work for it. That's part of what makes us special. That's what keeps us at the forefront of business and science and technology and medicine."
Obama said 60 percent of new jobs in the next 10 years will require higher education, making it a necessity to make college affordable.
"So in a 21st century economy, a college education should be available for everybody -- not just the wealthy few," he said.
Before delivering his remarks, Obama stopped at Sloopy's Diner at the Ohio Union, where he glad-handed students and ordered a Reuben sandwich with potato chips and a piece of Buckeye Pie (peanut butter and chocolate filling with whipped cream).
As he left, students chanted "Fired up! Ready to go!" and he paused to take a group photo with three students pantomiming O-H-I-O -- Obama put his arms up for the I. Outside students cheered and chanted, "Yes we can."