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'Chill out,' give Obamacare a chance: Dem governor

The governor of Kentucky has some advice for Obamacare's critics—relax a little.

"Give us an opportunity. Take a deep breath. Chill out, and let this thing work," Gov. Steve Beshear told CNBC Wednesday.

As opposed to problems elsewhere, the Kentucky online Obamacare exchange has been "going gangbusters," he said.

"Unlike the federal exchange, things are working very well here," Beshear, a Democrat, said in a "Squawk Box" interview.

(Read more: Langone to GOP: Shutdown gave party 'black eye')

Kentucky runs its own website for state residents to sign up for health insurance under the new law. Thirty-six other states chose to have their residents enroll through the federal portal, Healthcare.gov, which has been plagued with technology problems.

The Kentucky online exchange has had more than 350,000 unique visitors. There have also been about 70,000 phone calls to the help-center hotline. Almost 32,000 residents there have signed up for either the Medicaid program or the qualified health plans.

"By the way, a third of the people signing up for both the qualified health plans and Medicaid are under 35 in Kentucky," Beshear added. Participation from younger people—who are presumably healthier and won't use their benefits as much—are needed to offset the expected costs of the more frequent needs of the elderly and the sick.

(Read more: Obamacare can't make health care cheaper: Langone)

"We've got another 12,000 people who have already determined that they qualify for the subsidies and they're now just shopping," he said. "They will start signing up."

He said the enrollment numbers break down as about two-thirds Medicaid and one-third qualified health plans, though that is expected to even out.

"It's going to take some time. If you go back and look at the last time there was a transformational change in our health-care system in the United States, it was the Medicare Act in 1965. It look about three years for all those bumps in the road to be smoothed out," he said, adding that he expects the same of Obamacare.

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

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