Americans unconvinced about Obamacare: NBC/WSJ poll

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Three and a half years after the passage of the Patient Protection and Affordable Care Act – also known as Obamacare – , Americans remain unconvinced that it will improve their own health care or the nation's, according to an NBCNews/Wall Street Journal poll.

The survey results come as the Obama administration and states prepare to offer insurance through "health insurance marketplace." Their ability to persuade Americans that are currently uninsured to sign up will be critical to the ability of those marketplaces to keep rates affordable.

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Just 31 percent of Americans say the new health law a good idea, while 44 percent say it is a bad idea. The proportion of those praising the law has declined from 36 percent three years ago.

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Uncertainty about the law may be part of the problem. Only 30 percent say they understand how the law will affect them, while 69 percent say they do not.

In any case, just 23 percent say the law will have a positive impact on the country's overall health care system, while a mere 12 percent say it will have a positive impact on their family.

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Perhaps most worrisome of all for the White House, 52 percent believe the cost of their health care will go up as a result of the law.

The telephone survey of 1,000 adults,conducted Sept. 5-8, carries a margin for error of 3.1 percentage points.

—By CNBC's John Harwood. Follow him on Twitter: @JohnJHarwood