Obamacare stuck in government 'abyss': Health CEO

EHealth CEO withdraws support for Obamacare

The White House needs to embrace a public-private sector partnership in order to keep Obamacare from unraveling, a former supporter of the health-care law told CNBC on Tuesday.

Gary Lauer, chairman and CEO of Internet-based health insurance broker eHealth, said he no longer has confidence Obamacare can work in its current state. "We're stuck in this kind of abyss where it's all being left to government to do this. And just it's not going to work that way."

Consumers can come to eHealth for insurance, but Lauer's company is unable to process subsidies.

"If you're lower income right now, you can only go to a government-run exchange," he told "Squawk Box."

"It's much like saying, 'If you're low income, you can only ship a package through the Postal Service. If you're higher income, you can use FedEX or you can use UPS,'" he added. "We're working with the federal government to change that, and trying to get a few states to come around."

The eHealth chief's comments came a day after the government said it will exempt companies employing between 50 and 100 full-time workers for another year, until 2016, from complying with the mandate that they offer employees affordable health insurance.

(Read more: Obamacare delay: Smaller employers get reprieve)

Lauer said he changed his opinion after watching President Barack Obama's Super Bowl interview in which he said there were no more significant issues.

"If you look at the enrollment numbers through the first 90 days, you really do have an imbalance there. You've got a number of older people, not enough younger people," he said.

Whether Obamacare can succeed or not may become known within the next six months, Lauer said, because insurance companies will soon start pricing their products for the next year. "This is really going to come down to what the enrollment looks likes and what the pricing of these products is as a result."

(Read more: Social Security computer outage to affect HealthCare.gov)

While acknowledging that the initially troubled federal Obamacare website is working pretty smoothly now, he said he's concerned about some of the state-run exchanges. "Some seem to be working OK, like California and New York, on a relative basis. And some are just a disaster."

Despite his criticisms, Lauer said he wants the health-care law to succeed.

By CNBC's Matthew J. Belvedere. Follow him on Twitter @Matt_SquawkCNBC.