(The following grew out of a discussion with two Chicago students doing an "independent study" in advanced general jurisprudence: 3L Courtney Cox and 2L Phil Smoke. They are not responsible for what follows, but I was helped by discussing the paper with them.)
Mark Greenberg (UCLA) has recently published a paper that synthesizes some of his earlier work and articulates his positive view in some more detail than previously. He calls his view "The Moral Impact Theory of Law," though for reasons I will make clear, I'm not sure this amounts to a theory of law except in some odd stipulative sense. (I will note my agreement with the criticisms articulated by Brian Bix [Minnesota], especially his observation that it is not controversial that the actions of legal officials can alter our moral obligations, but it is controversial, and unmotivated, to say that only the resulting moral obligations are the actual content of the law. I will try not to belabor that point, but rather to raise some other doubts.)
A few preliminary observations:
1. It's unclear what the criteria of success are for a theory of law on Greenberg's view. Positivists from Hart onwards wanted to do some justice to ordinary or commonly shared ideas about law, making explicit what was inchoate and correcting various tensions in ordinary thought and talk about law. (See the discussion in Langlinais & Leiter.) It's plain that this is not Greenberg's criterion. Indeed, he specifically disowns considerations of "English usage or even lawyers' intuitions" (1338), and he has to since he claims that on his view "the law can never include truly evil norms," among other wholly counter-intuitive claims (1337). He says that a "true" theory can have "counterintuitive consequences," and justifies that by noting that "a great deal fo what we now think about the world and about human beings would once have been thought to be absurd" (1338). That's true, but we know roughly what the criteria of success were for counterintuitive physical, biological and psychological theories, e.g., their explanatory and predictive power. Greenberg's view has no explanatory power as far as I can see (it obviously does not aspire to predictve power). I return, below, to what little he says about the supposed virtues of his theory (see [B], below).
2. Greenberg's view depends on a quite extravagant form of moral realism, which is undefended (and, in my view, could not be defended). And this extravagant and undefended moral realism leads him to say things like: "it is a general moral truth that, to the extent that people have equal opportunity to participate in procedures of governance, they acquire moral reasons to comply with the decisions that are reached through those procedures" (1313). That this "general moral truth" is contested by many political philosophers does not give Greenberg pause. I was also genuinely shocked to see Greenberg say "that much of our concern with law presupposes that...[moral] skepticism [or anti-realism] is false" on the grounds that the anti-realist believes that "people have interests and desires and wield raw power, but there is no reason to be concerned with unfairness, inequality, cruelty, or injustice" (1308 n. 43). As fraudulent libels of moral anti-realists go, this one is at the head of the class! I have to wonder whether bad student editing played a role in this strange footnote.
3. Greenberg repeatedly makes claims about the "functions" of law and about law's "nature," but offers no defense of them, no explanation of how it is an artifact can have essential functions or even a nature. Claims about what seems "natural" or "plausible" or "intuitive" do far too much work in this paper, and most of the claims said to be "natural" or "plausible" or "intuitive" do not seem to me to be anything of the kind: they range from the idiosyncratic to the debatable. (A partial catalogue of some of the astonishing, and undefended, claims of this kind: "it is part of the nature of law that a legal system is supposed to change our moral obligations to improve our moral situation" ; "a legal system, by its nature, is supposed to change the moral situation for the better" ; while allowing that, in fact, "it is controversial what the functions of law are, or even whether law has functions"  he then claims "for purposes of argument" that "settling disagreements is an important function of law"  and that it is "at least as plausible" that law's other functions include "that government coercion is used only in accordance with past political decisions," that law is "acting for the public good," and (of course) "improving our moral situation" .)
Now some more specific questions and doubts:
A. Greenberg claims that most theorists accept "the Standard Picture" according to which "the content of the law is primarily constituted by linguistic (or mental) contents associated with the authoritative legal texts" (1296) or, later, "working out an appellate decision's contribution to the law [is] a matter of identifying an authoritative text...and then extracting its linguistic content" (1316). In fact, I can not think of any theorists who accept "the Standard Picture" so defined. Greenberg's confused criticism of legal positivism brings this out. Greenberg writes:
[L]egal positivism does not specify how social facts determine the content of the law. To say that the content of the law is determined, at the most fundamental level, by social facts alone does not yet tell us, for example, how statutes contribute to the content of the law. One manifestation of this gap is that positivism by itself does not yield an account of statutory interpretation--of how to discover a statute's contribution to the content of the law. (1298)
In fact, it is precisely a virtue of the positivist theory that it does not answer this question generally, since what counts as proper statutory interpretation varies by legal system: among the pertinent facts in a given legal system are often facts about what ways of extracting content from statutes are permissible. By contrast, Greenberg's view simply supplants whatever the local norms of statutory interpretation are in favor of a one-size-fits-all-model that claims "the question of legal interpretation" is always "what is morally required as a consequence of the lawmaking actions" (1303)--or later, "the contribution of a statute to the content of the law will depend on the on-blanace best resolution of conflicts between moral considerations" (1330)--views of statutory interpretation that are, I would venture, unrecognizable to most judges in most legal systems.
It bears noting, by the way, that even on Greenberg's view "the linguistic content of...texts is...one relevant consideration" in figuring out "the moral impact of" what the legal institutions have done (1303) and, indeed, he argues later that in some circumstances "the linguistic content of directives will be morally binding" (1315).
B. Greenberg adduces a few considerations that purportedly favor the "Moral Impact Theory" as a theory of law, rather than of something else. First, he says, "it is plausible [there's that word again!] that moral reasoning has a place in legal interpretation" (1304). Everyone agrees that moral reasoning has "a place in legal interpretation," what is in dispute is whether that place is necessarily required by the law. Second, Greenberg says, "legal systems treat legal obligations as genuinely binding obligations that are generated by the legal institutions" and claims his view "vindicates this treatment," whereas the positivist theory allows that "it can be true that one has a legal obligation despite the fact that one has no [genuine] obligation" (1304). I take it "genuine" means "moral obligation." Assuming that, Greenberg gets it exactly backwards: it is a virtue of a theory of law that it does not entail that every legal institution's claim to have generated a genuine obligation is vindicated. Disabusing people of the false notion that the law's commands are morally obligatory is both a practical and theoretical virtue of the positivist theory, as Hart noted long ago (cf. The Concept of Law, 207-212). Third, Greenberg says his view "makes it easy to explain our dominating concern with law" (1304) since, "If the legal institutions change what we are obligated to do, it is vital to work out that change" (1305). But this just returns us to Bix's point: it is true on everyone's view that what legal institutions do may affect our moral obligations, and that is one reason for being concerned with law. There are other reasons we are concerned with law, and other more obvious ones I would say: for example, the law can help us pursue our goals; the law may sanction us if we act in certain ways; and so on. All these mundane reasons for being interested in law are consistent with the positivist theory.
C. Greenberg is aware that his view, even as an account of a stipulative sense of "law," makes it puzzling what a legal institution is: it can't, obviously, be an institution created by the law, since the content of the law is just the moral obligations that result from what pre-existing legal institutions do. Greenberg takes the issue up at 1323 ff., but tells us very little. He notes, consistently with his earlier ex cathedra pronouncements, that it is "a necessary condition on a legal institution...that it be an organization that, by its nature, is supposed to improve the moral situation" (1324). One might think that is also true of, e.g., religious institutions, universities, reformatories, hospitals, and many other "organizations." Greeneberg recognizes that this "necessary condition" radically underdetermines what a legal institution is, but then invokes the fact that there is "a great deal of consensus about which institutions are legal institutions" (1325) That's true, something that positivist theories actually explain.