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President Obama defended his signature health care law Wednesday in a speech from Boston, saying that people who are losing their insurance plans because of the law should start shopping around for better coverage.

Speaking at historic Faneuil Hall, Obama acknowledged the problem-plagued rollout of ObamaCare and attempted to deflect criticism over the wave of cancellation notices hitting small businesses and individuals who buy their own insurance.

The cancellation notices apply to people whose plans changed after the law was implemented or don't meet new coverage requirements. The president said those changes ensure that all Americans are able to get quality coverage.

"So if you're getting one of these letters, just shop around in the new marketplace. That's what it's for," Obama said. "Because of the tax credits that we are offering, and the competition between insurers, most people are going to be able to get better, comprehensive healthcare plans for the same price or even cheaper than projected."

Republicans believe the president's argument flies in the face of his repeated claims that consumers who liked their insurance would be able to keep it.

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    Officials in Oregon say 150,000 Oregonians enrolled in individual health care plans will see their plans cancelled by the end of the year because the plans don’t provide the minimum level of coverage required under the new health care law.

    In Florida, about 300,000 Blue Cross and Blue Shield members will be affected. California’s Blue Shield and Oakland-based Kaiser Permanente will withdraw policies for a combined 280,000 customers. CareFirst Blue Cross Blue Shield sent notices to more than 70,000 customers in D.C., Virginia, Maryland and Washington whose current plans don’t comply with the law, according to Bloomberg News.

    Sens. Ron Johnson, R-Wis., and Marco Rubio, R-Fla., introduced legislation Wednesday aimed at giving American the ability to hold onto their plans if they liked them. The bill would add flexibility to the standards for insurance policies allowed under ObamaCare.

    "That was a fundamental promise that was made in order to get this law passed and now that’s being broken and we’re seeing that it wasn’t an unintended consequence, it was an intended consequence," Rubio told Fox News' Greta Van Susteren on “On the Record."

    The president's remarks marked a striking departure from his vow stretching back to 2009: "No matter how we reform health care, we will keep this promise to the American people. If you like your doctor, you will be able to keep your doctor, period. If you like your health care plan, you'll be able to keep your health care plan, period. No one will take it away, no matter what."

    And from the final months of the 2012 campaign: "If you're one of the more than 250 million Americans who already have health insurance, you will keep your health insurance. This law will only make it more secure and more affordable."

    Obama chose the site where Massachusetts' health care system became law to promote his health care law, arguing that the state plan also faced initial setbacks and low enrollment but in time gained popularity and became a success.

    "All the parade of horribles, the worst predictions about health care reform in Massachusetts never came true," he said. "They're the same arguments that you're hearing now."

    The president pointed to benefits already available under the 3-year-old health care law, including ending discrimination against children with pre-existing conditions and permission to keep young people on their parents' insurance plans until they turn 26.

    Romney took issue with Obama's characterization of the Massachusetts health care law. In a statement, he said "had President Obama actually learned the lessons of Massachusetts health care, millions of Americans would not lose the insurance they were promised they could keep, millions more would not see their premiums skyrocket and the installation of the program would not have been a frustrating embarrassment."

    Obama he conceded the troubled launch of the open enrollment period that began Oct. 1.

    "There’s no denying it, right now, the website is too slow, too many people have gotten stuck. And I am not happy about it. And neither are a lot of Americans who need health care, and they’re trying to figure out how they can sign up as quickly as possible," he said.

    Underscoring the president's challenge, the HealthCare.gov website was down, because of technical difficulties, during his remarks. Republicans say the current computer dysfunction is more reason to repeal the law, and they're pressing Obama administration officials for an explanation.

    The Associated Press contributed to this report.