President Obama tried a new tack Wednesday as he fought back against criticism of his Obamacare claims.

Fact-checkers and journalists have ruled that Obama wasn't being truthful when he claimed that people who liked their insurance could keep it. Obama during a speech in Boston sought to cast the issue Wednesday as trying to weed out "bad apple insurers" who don't provide enough coverage.

"One of the things health reform was designed to do was to help not only the uninsured but also the under-insured," Obama said. "And there are a number of Americans, fewer than 5 percent of Americans, who've got cut-rate plans that don't offer real financial protection in the event of a serious illness or an accident.

"Remember, before the Affordable Care Act, these bad apple insurers had free rein every single year to limit the care that you received or used minor pre-existing conditions to jack up your premiums or bill you into bankruptcy."

Obama said any such plans that existed before the health care law was passed can indeed be kept -- notably excluding plans that began after the law was passed.

"That's what I said when I was running for office. That was part of the promise we made," Obama said. "But ever since the law was passed, if insurers decided to downgrade or cancel these substandard plans, what we said under the law is, you've got to replace them with quality, comprehensive coverage because that too was a central premise of the Affordable Care Act from the very beginning."

Obama also said that he is responsible for fixing the HealthCare.gov Web site -- even as Secretary of Health and Human Services Kathleen Sebelius said earlier in the day that Obama isn't responsible for the botched Obamacare exchanges rollout.

"Right now, the Web site is too slow, too many people have gotten stuck, and I am not happy about it," Obama said at a speech in Boston promoting the similar Massachusetts health-care law.

Obama added: "So there's no excuse for it, and I take full responsibility for making sure it gets fixed ASAP."

The administration has set a late November deadline for fixing the Web site.

At a hearing earlier Wednesday, Sebelius said she and her department were responsible for the rollout's failings, not Obama.

"No, sir," Sebelius said when asked directly whether Obama is responsible. "We are responsible for the rollout."

Updated at 9:47 a.m.