Companies want to know more. "While the (private health insurance exchange) market has remained fairly nascent with fewer than 1 million enrollees in 2012, employers are expressing tremendous interest. Recent employer surveys indicate that more than 1 in 4 employers are considering moving to a private exchange in the next three to five years."

Plenty of insurance companies are crafting exchanges, which guarantees they eventually will be seen as mainstream products.

Understanding leads to acceptance. Some 85 percent of employers and employees who are educated about exchanges have a generally favorable sense about the concept. "Respondents are attracted to choice, flexibility, the personalized product selection and the shopping experience," Accenture said.

These factors add up to a "latent demand for the private exchange model," Accenture said, that "will further accelerate private exchange adoption."

The challenge remains to overcome employee misunderstandings about how exchanges work and how, specifically, they may be able to afford better health care for themselves and their families through an employer-sponsored private health exchange.

"Rapidly expanding private exchanges will increasingly enter C-suite conversations. Adoption has accelerated substantially, and will continue to do so as public and private exchanges demonstrate legitimacy and early vendors mature their offerings.

"However, this velocity of change will surprise a largely unaware consumer population. This may result in negative consequences for those who lack the education, support, and tools required to effectively manage increased responsibility for personal health care risk.

"Effectively addressing this latent demand and supporting consumer success are critical success factors for aspiring market leaders," the survey concludes.