Growing balances in health saving accounts are increasing consumers’ ability to see specialists and get X-rays, but that may be a double-edged sword, according to the director of a benefits research group.

Having more money set aside in the tax-advantaged accounts is helping consumers get needed care, but it also “may be inducing people to use health-care they wouldn’t otherwise use,” Paul Fronstin, director of the Employee Benefit Research Institute’s health research program, said in an interview.

There are about 25 million health savings accounts across the country, and concerns over wasteful spending could prompt employers to raise deductibles in...