It could take a "couple of years" to figure out the full costs of Obamacare to health-care providers, said Bernard Tyson, chairman and CEO of Kaiser Permanente—one of the nation's largest not-for-profit health plans, serving approximately 9.3 million members.

"We still have work to do better to understand the costs obviously because in most cases this is a new population in which they haven't had coverage before," he said on CNBC's "Squawk Box"on Monday.