A new poll by the Kaiser Family Foundation finds that public support for President Obama’s health care law has ticked down again, to just 35 percent. But even more striking is what the survey says about Americans’ knowledge of the law.

According to the poll, 42 percent of respondents think Obamacare has already been repealed/struck down by the Supreme Court or they don’t know enough to say whether it’s still law. The numbers are even worse among key subgroups. Among 18- to 29-year-olds, 51 percent couldn’t even identify the status of the law. This is a group of people who the law hopes to coax into the insurance system to help offset the costs of covering people with preexisting conditions. An even higher 59 percent of respondents earning less than $30,000 a year were aware of the law’s status. This is a group that is supposed to be among the primary beneficiaries of the law’s expansion of insurance coverage.

There are two ways of looking at these results. One is to say that these numbers suggest that public ignorance about the status of Obamacare may make it harder for Republicans to run successfully against the law in 2014. But another way of looking at it is that these survey findings provide a further challenge to the Obama administration as it seeks to implement the law and educate the public about it.