Even in a weak job market, the old college try isn’t the answer for everyone.

A briefing paper out Wednesday from the Brookings Institution warns that “we may have overdone the message” on college, senior fellow Isabel Sawhill said.

“We’ve been telling … students and their families for years that college is the only way to succeed in the economy these days and of course there’s a lot of truth to that,” Ms. Sawhill said. “On average it does pay off… But if you load up on a whole lot of student debt and then you don’t graduate, that is a very bad situation.”

One refrain amid the years of slow job growth has been the value of education for landing a job and advancing in a career.

April’s national unemployment rate stood at 7.5%, according to the Labor Department. The unemployment rate for high-school graduates over 25 years old who hadn’t attended college was 7.4%, compared with 3.9% for those with a bachelor’s degree or more education. The disparity is even bigger among those aged 16-24. The jobless rate for those with only a high school diploma in that age group is about 20%.