WASHINGTON—The federal government is on track to forgive at least $108 billion in student debt in coming years, as more and more borrowers seek help in paying down their loans, leading to lower revenues for the nation’s program to finance higher education.

The Government Accountability Office disclosed the sum Wednesday in a report to Congress which for the first time projected the full costs of programs that set borrowers’ monthly payments as a share of their earnings and eventually forgive portions of their debt.

The GAO report also sharply criticized the government’s accounting methods for its $1.26 trillion student-loan portfolio, pointing to flaws that have led it to alter projected revenues significantly over the years. The government says it still expects the program to generate a profit over the long term, but it has repeatedly trimmed expectations for revenues.

President Barack Obama has promoted income-driven repayment plans—passed by Congress in the 1990s and 2000s—to stem a sharp rise in borrowers defaulting on their loans since the recession. Enrollment in such plans has more than tripled over the past three years to 5.3 million borrowers, who owe roughly $269 billion, according to Education Department statistics cited by the GAO.

A new federal report shows that the government is expected to forgive at least $108 billion in student debt in the coming years. The relief is part of an Obama administration plan to help borrowers, but is proving costly. WSJ's Lee Hawkins explains.

Ted Mitchell, undersecretary at the Education Department, said such programs “are helping millions of borrowers successfully manage loan repayment, particularly those for whom standard repayment may prove challenging.”

He added that the administration has proposed changes to reduce costs. Mr. Obama, for example, has called for capping how much debt public-service workers can have forgiven.

The most generous version of income-driven repayments caps a borrower’s monthly payment at 10% of discretionary income, which is defined as adjusted gross income above 150% of the poverty level.

That formula typically lowers monthly payments of borrowers by hundreds of dollars. Public-service workers—those employed by a government agency or at most nonprofits—have balances forgiven after 10 years, tax-free. Private-sector workers have balances forgiven in 20 or 25 years, with the forgiven amount taxed as ordinary income.

President-elect Donald Trump said during his campaign he supported the idea of helping student-loan borrowers. He has proposed setting payments at 12.5% of income and forgiving balances after 15 years. He has also suggested winding down the federal student loan program and shifting lending to the private sector.

Growing evidence suggests many of the most hard-pressed borrowers—college dropouts who owe less than $10,000—aren’t taking advantage of the programs, while workers with graduate degrees, such as doctors and lawyers who don’t necessarily need help, are.

The figures that the GAO cites suggest the average balance of borrowers in income-driven repayment plans stands at roughly $51,000. That sum suggests a disproportionate share of those benefiting from the plans are graduate-degree holders. Undergraduate borrowers owe about $30,000, on average, upon graduation, other research shows, and the government caps lifetime borrowing from federal programs for undergraduates at $57,500. It doesn’t limit how much grad students can borrow. And graduate-degree holders typically have higher incomes and have low rates of unemployment, Labor Department data show.

There are still about 8 million Americans in default on their student loans, and the number of defaults among borrowers who recently left school has come down only slowly.

Meanwhile, Senate Budget Committee Chairman Mike Enzi (R., Wyo.), who ordered the GAO study, has criticized the Obama administration’s use of executive authority to sweeten terms of the repayment plans, which he said would add to the national debt.

“This Administration has been manipulating the terms of the student loan program without the consent of Congress, while shirking its statutory duty to carefully assess the cost impact of those changes,” Mr. Enzi said in a statement, adding that he was considering legislation to force changes in the government’s accounting methods.

Some outside academics say it is increasingly likely that the projected surpluses of the federal student loan portfolio—which has more than doubled over the past decade—won’t materialize. “I’m not at all confident that the federal government will end up making money on student loans,” said Robert Kelchen, an assistant professor of higher education at Seton Hall University.

In addition to debt forgiveness under income-driven repayment programs, the administration is also moving to forgive loans for borrowers who can show they were lured to enroll at schools—mostly for-profit colleges—that used deceptive advertising.

Students at the Rutgers University graduation ceremonies in Piscataway, N.J., in May. Photo: Mel Evans/Associated Press

Income-driven repayment plans are also causing concern that as more students become aware of the benefits, they will become less sensitive to tuition increases, enabling universities continually to raise tuition ultimately at taxpayer expense. Higher education costs have increased by an average of 5.2% a year in the past decade, far faster than inflation, which has been running at under 2%.

And some borrowers with graduate-school loans are refinancing their debt at lower interest rates with private lenders such as SoFi. Congress, through legislation, has set higher interest rates for grad students than undergrads, to ensure the programs don’t lose money. When private lenders pick off those borrowers, the surpluses dwindle.

The GAO estimates $137 billion owed under income-driven repayments won’t be repaid. Most of it—the $108 billion disclosed Wednesday—would be forgiven because of borrowers fulfilling their obligations under the plans. The other $29 billion will be written off because of disability or death, the GAO projects, the only other circumstances under which the government takes a loan off its books. The government can garnish wages and Social Security checks for those in default.

And that $108 billion only covers loans made through the current fiscal year. The overall sum could continue to grow alongside enrollment increases. The GAO said it could take 40 years to know the full costs of the programs.

Still, supporters say the plans offer a lifeline to borrowers who are unemployed or earning little, while the Obama administration has credited the programs with leading to a reduction in the number of new graduates defaulting on their loans.

Supporters point out that under current law, any amount forgiven would be taxed as ordinary income for private-sector workers, limiting the benefits for individuals. Public-sector workers aren’t taxed on forgiveness.

The GAO report also criticizes how the Education Department has produced budget estimates for the loan program. For example, it said the department has failed to account for inflation when estimating borrowers’ future earnings. And it said the agency failed to account for further increases in enrollment in income-driven repayment plans.

Write to Josh Mitchell at joshua.mitchell@wsj.com

Corrections & Amplifications:

Borrowers enrolled in plans that forgive student debt owe an average of about $51,000 and a combined $269 billion, according to Education Department statistics cited by the Government Accountability Office. An earlier version of this article incorrectly said these borrowers owed an average $67,000 and a combined $355 billion. (Dec. 2, 2016)