Not among the American public. Though public opinion polls are collecting information about the public's attitudes towards the economy and whether they prefer capitalism, socialism, or a free market, there are reasons to believe that people have no consistent understanding of what these terms mean.
I've asked these questions in class before and found that "socialism" general equates to "bad things that Obama is going to do as president."
While my students consider the nature of public opinion in America, it is worth considering whether people have enough background about basic facts to form well founded opinions, rather than superficial off the cuff responses to questions, or repetitions of comments heard elsewhere.
My 2301's should consider the post linked to above required reading.
