Less than one in five Americans say their families will be better off under the new health care law, according to a new CNN poll.

But a CNN/ORC International survey released Tuesday morning also indicates a majority say the Affordable Care Act, better known as Obamacare, will help some people, with 37% saying the law, which is gradually starting to kick in, won’t help anyone.

According to the poll, four in 10 say the new law will make their families worse off, while 41% believe it will have no effect.

Seventeen percent think the measure will be a good thing for themselves or their families.

The poll’s release comes on the same day as a key element of the health care law takes effect, as Americans without insurance can begin enrolling in state insurance exchanges.

And it comes hours after the shutdown of the federal government courtesy of a bitter partisan battle over the new health care law.

According to the poll, 36% say they won’t benefit from the new law but other families will. If you add to that the 17% who believe Obamacare will help them personally, the survey indicates that most Americans see some good coming from it. Some 37% say no one in the country will benefit from the measure.

As the exchanges open for business, 52% say the health insurance system created by Obamacare is a disaster waiting to happen, with 45% saying the system will eventually work.

The poll was conducted for CNN by ORC International September 27-29, with 803 adults nationwide questioned by telephone. The survey’s overall sampling error is plus or minus 3.5 percentage points.

With most components of the health care law not taking effect until 2014, many Americans still don’t have a full grasp of Obamacare, and a couple of surveys from other organizations conducted in September indicated that only a minority said they knew a lot about the law.

The Men’s Divorce Law Firm urges you to learn more about the Affordable Care Act so that you know what your family’s rights and benefits are.