Nearly 7 million Americans have gone at least a year without making a payment on their federal student loans, a high level of default that suggests a widening swath of households are unable or unwilling to pay back their school debt.

As of July, 6.9 million Americans with student loans hadn’t sent a payment to the government in at least 360 days, quarterly data from the Education Department showed this past week. That was up 6%, or 400,000 borrowers, from a year earlier.

That translates into about 17% of all borrowers with federal loans being severely delinquent, a share that would be even higher if borrowers currently in school who aren’t yet required to repay were excluded. Millions of other borrowers are months behind but haven’t hit the 360-day threshold that the government defines as a default.

Severe delinquencies are rising despite the sharp drop in unemployment over the past year and a big push by the Obama administration to enroll borrowers in programs that lower their monthly payments. Delinquencies on other types of debt such as credit cards and mortgages have fallen. And shorter-term defaults on student loans have declined over the past year.

The latest figures highlight how student debt—which has tripled over the past decade to $1.19 trillion, according to the Federal Reserve Bank of New York—has quickly become a crushing burden for more Americans.

Derek Lance, 31 years old, says he had gone more than a year without paying down his student debt, which now stands at about $70,000. At the time of his payment lapse, he had been paying high rent in San Francisco and was making little in his job. “I figured I wasn’t going to be able to make payments, so I kind of just brushed it off to the side,” said Mr. Lance, whose loans covered college and grad school.

After learning that his mother, a co-signer on the loans, might become the target of debt collectors, he moved into a cheaper place with roommates and began making payments last year. The freelance charity fundraiser and marketer is now paying $1,100 a month toward his student debt.

“There’s plenty of people out there who feel like they’ve been ripped off, and the notion of repaying the loan for 10 or 15 years is just impossible for them,” said Jason Delisle, a higher-education expert at the New America Foundation, a think tank. “If this were happening in the corporate sector it would be an economic catastrophe, if you had defaults of that rate.”

The growing number of yearlong-plus delinquencies carries sizable implications for borrowers, taxpayers and the economy. Economists have warned about student-debt defaults damaging borrowers’ credit standing, constraining their ability to borrow for things like cars and homes for years. That in turn would hamper the economy, which relies heavily on consumer purchases for economic activity. Delinquencies also drain government revenues, which are used to make future loans.

The student-debt boom has helped many households and hurt others, a divide highlighted by the default data.

Those in default owe relatively little—a median $8,900, according to the Education Department. Other figures show that borrowers who attended for-profit schools—who are disproportionately minorities—account for a disproportionate share of defaults. Many borrowers in default dropped out of school, leaving them with debt not the degree that typically boosts incomes.

Conversely, student debt has helped other households earn bachelor’s and advanced degrees, boosting their lifetime incomes and quality of life.

A significant number of borrowers in default never made a single payment, experts say.

Navient, one of the servicing companies that collects debt payments on behalf of the government, said that 90% of federal borrowers who default never talk to the company in the year in which they default, despite repeated attempts from the company to reach them.

The Obama administration didn’t address the defaults in releasing the data. Instead, Education Department officials pointed to figures they said showed progress in getting some Americans current on their bills.

Shorter-term defaults—those in which borrowers have gone between 31 days and 359 days of making no payment—declined over the past year, the agency said. Among those who borrowed directly from the government—the majority of those with federal loans—the share who are least 31 days behind fell to 21%, from 23% a year earlier. A similar drop occurred among borrowers under a now-defunct program that provided government guarantees for privately made student loans.

About 17% of students with federal loans haven’t made a payment in a year even as the economy was rising.

Education Secretary Arne Duncan said those declines resulted from rising participation in income-based repayment plans, which lower borrowers’ monthly bills by tying payments to their incomes. Enrollment in the plans surged 56% over the past year among direct-loan borrowers.

“The fact that more and more borrowers are taking advantage of the opportunity to cap their monthly payments is a good sign,” Mr. Duncan said.

The administration has heavily promoted the plans, including through emails to borrowers, over the past two years in an effort to stem defaults. The plans set payments as 10% or 15% of their discretionary income, defined as adjusted gross income minus 150% the federal poverty level.

But research shows that the biggest beneficiaries of the plans are likely to be big-ticket borrowers—mainly those who went to graduate and professional schools and who are likely to earn more than those who only have bachelor’s or who dropped out.

Denise Horn, an Education Department spokeswoman, said the administration is trying to reach defaulted borrowers to make them aware of options to lower their bills, such as income-based repayment.

“We are doing everything we can to be responsive to students’ needs,” she said. The agency has set up a system for borrowers to file complaints about servicers who aren’t responsive, and it is analyzing student-debt trends to glean more details of defaulters.

The government also contracts with companies to track down borrowers in default and has the power to garnish wages, tax refunds and even Social Security checks for repayment.

The income-driven repayment plans carry risks for both borrowers and the government. Many borrowers’ payments aren’t enough to cover the interest on their debt, allowing their balances to grow and threatening to trap them under debt for years.

At the same time, the government could be left forgiving huge amounts of debt if borrowers stay in the plans. The government forgives balances after 10, 20 or 25 years of on-time payments, depending on the plan.

The administration maintains that the overall student-loan program will generate long-term profits for taxpayers, but it has recently revised down revenue estimates by billions of dollars due to growth in the income-driven plans.

The administration is trying to grapple with long-term defaults. It’s not clear why so many borrowers aren’t making payments, though there are several theories.

Christa Labanara, a counselor for the nonprofit American Student Assistance who is in contact with defaulted borrowers, says many are unemployed and in low-paying jobs and juggling bills. “They’re not finding the jobs that they thought they were going to get paid,” Ms. Labanara said. “It’s like, ‘What comes first? Does my mortgage come first or my student loans?’ ”

Data on defaulted borrowers is limited. Mr. Delisle organized a focus group of such borrowers to learn their circumstances. Some borrowers won permission from the government to temporarily postpone payments, and planned to eventually repay. But when they saw the balances grow quickly, they felt hopeless, he said.

Others felt their schools didn’t deliver on their promise of a quality education. When they didn’t get they jobs they expected, he said, some refused to pay. “They feel like they didn’t’ get what they paid for,” Mr. Delisle said.

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