And the people most likely to benefit from the health insurance exchanges and subsidies are often least likely to be aware of them.

The survey was conducted between July and September, and released just one day before the exchanges launched.

Only 32 percent of people without health coverage during the past year are aware of the exchanges, compared to 43 percent of the insured.  Thirty-one percent of people without coverage during the year are aware of the subsidies that are available, compared to 43 percent of those insured all year.

Just under one-third (32 percent) of adults with incomes under 250 percent of the federal poverty level ($28,725 for an individual and $58,875 for a family) are aware of the subsidies, compared to 47 percent of those with higher incomes.

But the good news, Commonwealth researchers said, is that once people are made aware of the exchanges, 61 percent said they are "very" or "somewhat likely" to shop for coverage through them. That number, though, falls for young adults and adults with no health problems.

Commonwealth's survey is nothing new, as confusion has plagued PPACA since its passage. But it's worrisome as Tuesday's exchange launch marked a big milestone for the law.

Meanwhile, other recent polls don't bode well for the law.

Kaiser Family Foundation and NBC found that just over half are worried about the health care law, with most concerned they would pay higher health care costs as a result of the law's main provisions.

A CNN/ORC International survey released Tuesday found that fewer than just one in five Americans say their families will be benefit from PPACA.