Bethany College in Lindsborg, Kan., this past year offered a 12-month plan that cost students $445, while capping payouts at $10,000. For the 2012-13 academic year, the Obama administration said the payout cap must be at least $100,000. Bethany said students would have had to pay more than $2,000 to get that new level of coverage.

“We decided not to offer coverage for our students next year given the proposed increase in premium,” said Bob Schmoll, Bethany’s vice president for finance.

Mr. Schmoll said his school wished it could have kept the limited-coverage plan, which he said was a “fairly robust program for the type of need that most students of that age have.” Even the old premium was “for many a struggle to pay,” he said. Students previously had to sign up for the school’s plan if they didn’t have other insurance. Now students won’t be required to have health coverage.

The new rules are likely to affect a broad swath of American colleges, particularly small ones. Some 60% of schools’ plans had coverage of $50,000 or less for specific conditions, and almost all of the rest had some sort of payout caps that they will have to do away with by 2014, the GAO study found.