The rollout of Obamacare has been "absolutely chaotic," said Tommy Thompson, who served as U.S. Health and Human Services secretary under George W. Bush. But worse, he added, the new law is flawed and needs dramatic changes. "It's actuarially unsound," the former Republican governor of Wisconsin said on CNBC's "Squawk Box" on Tuesday. "If you don't have the healthy young people involved, ... Obamacare cannot function. It's going to require a huge infusion of tax dollars or huge cuts." One of the cornerstones of the new health-care law is that healthy young people will pay for medical insurance that they use less frequently than the elderly or the chronically ill. But, Thompson said, from the view of a healthy young person, they may ask: "''Why do I want to do that?''" Under Obamacare, most Americans have to buy insurance or face a tax penalty.

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Senator Tommy Thompson, R-WI Getty Images

While at HHS, Thompson said he was responsible for pushing the Medicare Prescription Drug Plan (Part D) into law "on a bipartisan basis" a decade ago. Addressing critics who say Medicare Part D has been a flawed endeavor, Thompson stood by it. "Part D was correct. If you look at the actuarial soundness of it, you'll find that it's even better than any of the estimates ever predicted." "We've saved money every single year under Part D," he said—adding that in addition to "quarterbacking" Part D, he also was responsible for setting up the work necessary to implement it. Looking at Obamacare through that prism, Thompson told CNBC what he would change. "We cost too much on administration. We've got to cut that back. We've got to cut back on the paperwork, the rule-making. We've got to be able to have refundable tax credits," he said. "We've got to allow the insurance companies to make some rating decisions."