DRAPER, Utah—Mike Meru, a 37-year-old orthodontist, made a big investment in his education. As of Thursday, he owed $1,060,945.42 in student loans.

Mr. Meru pays only $1,589.97 a month—not enough to cover the interest, so his debt from seven years at the University of Southern California grows by $130 a day. In two decades, his loan balance will be $2 million.

He...