Less than a week before the health insurance marketplaces established by the 2010 health care law begin accepting customers, a New York Times/CBS News poll has found that there is some support among uninsured Americans for President Obama and his law, but also a wariness and a lack of understanding about what the law will mean for them.

Uninsured Americans are divided about whether the law will help them, with 3 in 10 saying it will affect them positively, and about the same percentage saying it will hurt them. Four in 10 say it will have no effect on them. Six in 10 say they find the law confusing.

However, nearly 6 in 10 uninsured Americans say they trust Mr. Obama over Republicans in Congress on health care, and more than two-thirds do not want the law stripped of its financing.

 As the Obama administration continues its campaign to convince millions of uninsured Americans that they will benefit from the law, the poll shows that skepticism remains: a majority of Americans disapprove of the law, half say they find the law confusing, and nearly half expect it to hurt the economy over the long run.

Fewer than 4 in 10 Americans approve of the law, and among Democrats, two-thirds approve. More than half of independents and more than 8 in 10 Republicans expressed disapproval.

Although Americans do not appear to be rallying around the law, the poll showed that there is stronger support for keeping the law in place and making it work as well as possible than for trying to stop the law and remove its financing.

Understanding of the health care law is one problem: just one in five Americans say they know a lot about it.

Perception of the law’s impact breaks down largely along party lines: 7 in 10 Republicans think the law will hurt them, compared with just one in five Democrats and more than a third of independents.

Similarly, a plurality of Democrats say the law will improve the national economy, while 8 in 10 Republicans and half of independents see the law as harmful to the economy.

The national poll was conducted Sept. 19-23 by landline and cellphone among 1,014 adults, and it has a margin of sampling error of plus or minus 3 percentage points.