President Obama should fulfill the promise he made that Americans could keep the health insurance they have, even if it means changing the Affordable Care Act law, former President Bill Clinton said in an interview published today.

"I personally believe even if it takes a change in the law the president should honor the commitment the federal government made to those people and let them keep what they got," Clinton told OZY, an web magazine, backed by Steve Jobs' widow, Laurene Powell Jobs.

Clinton told the story of a young man who he said he had his insurance policy cancelled and replaced with a new one with premiums twice as high. But because his co-pays and deductibles are lower, Clinton said the man might still save money if he and his family actually use their insurance. Clinton suggested though that the man should have been able to keep his old policy based on Obama's promise.

Clinton also compared the Affordable Care Act's roll out problems with Medicare Part D's flawed roll out during President George W. Bush's administration.

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"This happened once before, it happened when President Bush put in the drug program for seniors, which was not as complicated but had exactly the same problem with the roll out," Clinton said. "It was a disaster."

"And they fixed it," he added.

President Obama last week walked back his previous promise on the health care law that "if you like your health plan, you can keep it."

"One of the reasons that we took up health care reform was not just to help the uninsured, but also the underinsured or the badly insured," Obama told supporters at an Organizing for Action event in Washington, D.C.

Obama explained that if you have or had a substandard plan before the Affordable Care Act became law and "you really liked that plan, what we said was you could keep it, if it hasn't changed since the law passed."

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In selling the Affordable Care Act to the American public, the president often repeated the same refrain: "If you like your plan, you can keep your plan," he said in St. Charles, Mo., March 10, 2010.

Now, with hundreds of thousands of Americans receiving cancellation notices, the president has come under fire for misleading the American public. Obama said he understands it must be "scary" for Americans receiving these letters, but assured consumers that "we are making the insurance market better for everybody."

With reporting by ABC News' Mary Bruce.

(Peter Foley/Bloomberg via Getty Images)