WASHINGTON—The senator overseeing U.S. education policy said Congress should consider reinstating limits on how much graduate students can borrow and reducing loan amounts for certain categories of undergraduates, due to concerns the government is allowing students to amass debt too easily.

Sen. Tom Harkin (D., Iowa), chairman of the Senate Committee on Health, Education, Labor and Pensions, said he was concerned that a 2006 law to remove borrowing limits for grad students has helped fuel the surge in student debt. Before the...