Others say education is intrinsically expensive. Health care costs, for instance, have taken a toll, since colleges are labor-intensive. And the expense of keeping up with technology, like wireless Internet and new computers, is high. Here at Ohio State, where tuition has increased by nearly 60 percent since 2002, there is a gleaming new student union, climbing walls that can accommodate 50 students at a time and $2 billion in construction projects under way.

Mr. Gee’s compensation package this year, moreover, is worth about $2 million, and The Chronicle of Higher Education has called him the highest-paid public university president. The Dayton Daily News recently reported that Mr. Gee had billed Ohio State for $550,000 in travel in the last two years.

The travel expenses prompted some to question if Mr. Gee practices what he preaches.

“He’s very capable. He’s a very smart guy, and he’s engaging and all these things,” said Dale Butland, a spokesman for Innovation Ohio, a nonprofit policy research group. But he added, “Students and their parents who are struggling, not just with coming up with the money, but paying off the debt, I think there is a disconnect between what they are being asked to do and what they are seeing the leader of the university doing.”

Mr. Gee maintains that Ohio State is getting its money’s worth. On his watch, Ohio State has become a more prestigious university, he says, while remaining a relative bargain, even with fewer resources from the state. It now receives just 7 percent of its budget from the state.

Ohio State costs about $25,000 a year for in-state residents who live on campus. The average debt for graduates who borrow is $24,480.

A lanky 68-year-old who is known for his bow ties, horn-rimmed glasses and sometimes zany antics (he has shown up, unannounced, at 21st birthday parties for his students, which he finds on Facebook), Mr. Gee has had the top job at five universities, including twice at Ohio State. He returned to the Columbus campus in 2007 after stints at Brown and Vanderbilt. Mr. Gee acknowledges that college affordability and student debt are growing problems that university presidents long ignored. He said they now needed to address them quickly.

“We have not been as conscious about costs as we should be, and that has now come home to roost,” he said.