The federal health reform law, if it stands, should trim the number of uninsured Americans to about 5%, according to an Oliver Wyman survey.

The survey, exploring the effect of the Patient Protection and Affordable Care Act, passed in March 2010, on health insurance coverage, found that three-quarters of Americans without health insurance are likely to obtain coverage starting in 2014. In January 2014, states must provide health exchanges, where individuals and small businesses can compare health plans, buy coverage and obtain federal subsidies.

Under the federal health reform law, roughly 33 million Americans will be required to purchase health insurance for themselves. (Another 18 million uninsured will be eligible to receive coverage under Medicaid.) Many will receive federal subsidies, and those who choose not to obtain coverage will pay a penalty.

About 50 million Americans are uninsured, according to federal estimates.

Exactly 76% of respondents chose to purchase insurance. “Our research shows that uninsured Americans overwhelmingly see value in coverage,” Terry Stone, a partner in Oliver Wyman’s Health & Life Sciences practice and one of the study authors, said in a statement.. “But few really understand their options or even what a healthcare exchange is. They need to be educated.”

The uninsured, according to the survey, are “extremely price-sensitive,” meaning federal subsidies will play a major role in keeping consumers in the program. However, if falling subsidies drive consumers back to the ranks of the uninsured, middle-income consumers will suffer more than poor consumers, researchers found..

Consumers are ready to make tradeoffs to get the kind of coverage they want and need at a price they can afford—paying more for convenience and access, or agreeing to lifestyle changes for a discount. That is encouraging news for reform’s next goal: to encourage innovation in the way care is delivered, according to the survey results.

But the health reform law faces more than 20 ongoing court challenges, as well as attacks by Republicans seeking the nomination for president next year.