Jonathan Bernstein argues that independents do not know what "deficit" refers to, to explain how it can be that independents seem to favor a plan to tackle the deficit along the lines of the White House plan as compared to Paul Ryan's, but disapprove the White House plan more. Kevin Drum goes less far by saying that independents do not understand what Obama's plan is.
I lean towards Bernstein's position on this one. My opinion, based on no statistics at all, is that most people don't know and don't care. You can think it's a good thing or a bad thing, you might think of solutions to change this, but that's not really the question. From a paper by Suzanne Mettler, 40% of Americans do not think that Medicare comes from the government
and from a poll last December, via Ezra Klein, the classic foreign aid statistic:
And it goes on and on and on. I think the important is how easy you can turn a topic in a populist way, by throwing simple intuitions that are completely invalidated by facts. That's what happens with immigration(people come and take your job so we should not have immigrants. Also, they burn stuff), and that's what happen with the deficit(the gvt spends too much, it's bad, because most of it is waste).