Well, SC, we probably do agree on a few things then. In particular, I do agree with you that many people reach their opinions on issues of Constitutional law or on Supreme Court rulings based more on their political desires than on any knowledge of or interest in the law.
We would part ways on a couple things, though. Even by your usage of deep (which I guess is a less aggressive usage than I assumed, if you would consider my understanding deep ;-)), I don't necessarily agree that a deep understanding of the law is required to at least _begin_ to form good opinions in cases. A mere determination to judge them based on actual legal principles should be a sufficient beginning. A well written opinion and dissent should then lay out the arguments well enough to form a first opinion. Yes, of course a better understanding of the cases cited, etc., will enable a more accurate and fuller understanding, but it may be that even at the level of understanding one can gain from the opinion, one can decide that one side's reasoning is unconvincing. (Of course, I'm assuming a fairly accessible field, like the one today; if it's securities law, or even fourteenth amendment jurisprudence, then yeah, you probably want at least some background, unless the opinion is truly expository).
Interesting, as many noted today, the Chief Justice's opinion in the healthcare cases was unusually expository, presumably because he knew that many would read it.
The other place where we might or might not disagree is where you say that one should understand precedent well in order to come to a conclusion about the Constitutionality of a bill. That is true if you hold to certain views of the Constitution. But if one is, for example, an originalist who does not believe in stare decisis (like Justice Thomas) -- and that is a position that anybody could conceivably come to -- then one might well be able to make a conclusion about a given opinion without knowing the precedents involved, so long as one was passably familiar with the Constitution. Of course, that relies on a particular judicial philosophy which you may or may not find convincing, but it at least is not a retarded philosophy, and one who holds it can do as I say.
So, for example, it's not clearly crazy for a layperson to have strong opinions about federalism or the balance of powers (in either direction -- originalism was just an example) and to think that if precedent contradicts those opinions, so much the worse for precedent. Of course, there are arguments that could then be brought to bear on that judicial philosophy, and the person might not defend it very well, but.... whew, I'm getting far afield. The long and short of it is, I think it is perfectly possible for laypeople to have opinions on the constitutionality of laws that is fairly cogent without being thoroughly grounded in precedent.