Consumers on the lowest-tier "bronze" plans could see some of the biggest jumps in prices if preliminary requests are ultimately approved. In some cases, insurers are abandoning the low-premium offering altogether.

A unit of CareFirst Blue Cross in Virginia said it will transition all of its bronze plan members to mid-tier, or so-called silver, plans in 2017. The switch will mean a 70 percent price hike for those customers, according to the company's rate request filing.

Bronze plans have been some of the biggest sources of losses for insurers because the low rates attract sick patients who cost more, but often drop coverage during the year.

"Tons of people came in, got what they needed and left. And they ended up 20 percent — in some cases 30 percent — more expensive than those who came in and stayed," said Dr. Martin Hickey, CEO New Mexico Health Connections, a nonprofit cooperative insurer.

"With these heavy rate increases, the problem is the people who are going to say for a $695 penalty, to heck with it," Hickey explained. "The healthy abandon insurance, and what you're left with is the sick, and you can never raise your rates high enough."