Fewer than one-third of young, uninsured Americans say they are leaning toward enrolling in a health-care plan under the new Obamacare exchanges, according to a new poll -- a number that, if it holds, would present huge problems for the new law.

In order to keep costs down, the Affordable Care Act relies on younger, healthier people signing up for coverage to offset the costs for older, sicker Americans.

But a Harvard University Institute of Politics poll shows just 29 percent of uninsured 18-to-29-year olds say they will definitely (13 percent) or likely (16 percent) enroll in the Obamacare exchanges. When the question describes the law as the "Affordable Care Act" rather than Obamacare, just 25 percent say the are leaning toward enrolling or will enroll.