Linguists are still debating the force of "stimulus poverty arguments." This may never end, but a new rejoinder from Robert Berwick et al. (Chomsky is 4th author) appeared in Cognitive Science (2011 issue 7). In this article, the authors argue informally, but relatively correctly it seems to me, that a host of recent efforts to model the learning of language with virtually no prior assumptions about its structure in fact fail to account for the interesting structural constraints found in real languages.
They point out that recent proposals in Bayesian learning (Perfors et al. 2011) and learning of substitutable languages (recent papers by Clark and Eyraud) remain tied to string-based models of sentences, while the interesting syntactic constraints that are observed have to be represented using syntactic structure of some kind. This leaves the question unanswered, where do the structural constraints come from, and could they be learned? I think that some of my own recent work has addressed the issue of learning structures rather than strings, but then we have to learn from (at least partially) structured data, which presents its own plausibility problems.
An interesting point was brought up by my colleague Chris Golston, who is a linguist very interested in biology and evolution. He reminded me that stimulus poverty and learnability arguments have limited force in reality, because simply proving that a thing does not have to be innate, does not show it is not innate. A simple example comes to us from birdsong; it seems clear to everyone involved that birdsong is not that complicated and could theoretically be entirely learned, yet it is also widely held that birds harbor a considerable amount of innate propensity to sing a certain way. Not being a birdsong expert at all, it is possible I have misread the consensus in that field, but that's how I would summarize it for now. It is, I believe, quite likely that human language has this same general property---perhaps more of it is innate than really "needs to be" from a theoretical perspective.