Democrats have pointed to Kentucky's state health exchange as an Obamacare success story, but Sen. Rand Paul of Kentucky said on "This Week" that the system is "a mess," describing how his son was incorrectly enrolled in Medicaid, and saying he's unsure if his own family is currently covered.

"The other day I actually tried to get my son signed up through the Kentucky exchange, you know that the Democrats have said is so good. And I have here my son's Medicaid card," Paul told George Stephanopoulos Sunday, waving the card. "We didn't try to get him Medicaid, I'm trying to pay for his insurance. But they automatically enrolled him in Medicaid."

"I'm trying to pay for insurance and can't pay for it, and I'm uncertain now whether I'm enrolled in D.C. and/or Kentucky," Paul added. "And, it's a mess. I keep getting an error code every time I go in, it will not let me edit my policy to try to make sure that my family is covered… This is an unfolding disaster that I don't think gets better anytime soon."

Despite Paul's criticism, enrollments in Kentucky have surged since the launch of the exchange in October, going up 40 percent after Thanksgiving, and forcing state administrators to hire extra call-center workers and application processors.

But Paul, citing his own son's experience trying to get covered through the exchange, said most people signing up in the state are being enrolled in Medicaid.

"For a month they wouldn't talk to us because they said they weren't sure [Paul's son] existed. He had to go down to the welfare office, prove his existence, then the next thing we know we get a Medicaid card," Paul said. "So really, most of the people in Kentucky are being automatically enrolled in Medicaid."

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