What are the standard/best arguments against Construction Grammar?

Question

Introductions to Construction Grammar's "construct-i-con" model often include explicit arguments against the "lexicon and rules" model on the grounds that the latter is less equipped to deal with things like "the X-er, the Y-er" or "She sneezed the foam off her cappuccino" (to name two commonly used examples).

I'm interested in reading rebuttals of these arguments, and/or arguments against Construction Grammar for other reasons, from a lexicon-and-rules perspective. That is, articles that specifically say "Construction Grammar cannot account for phenomenon X, but lexicon-and-rules can" or "Construction Grammarians say that lexicon-and-rules can't handle phenomenon Y, but this is a misunderstanding and actually it can quite easily, as follows..." References to fully developed articles/essays/blog posts/books would be great if possible.

Answer 1

Charles Yang has argued against Tomasello's usage-based approach that underlies Construction Grammar. He explicitly pits item-based learning against rule-based learning in language acquisition. The argument is technical and based on quantitative evidence. The relevant papers are on his homepage: http://www.ling.upenn.edu/~ycharles/

Answer 2

There's a series of replies between David Adger and Adele Goldberg at lingbuzz:

http://ling.auf.net/lingbuzz/001633 http://ling.auf.net/lingbuzz/001675

Summing up two points of Adger's criticism: first, CxG admits hundreds of innate capabilities, such as innate capabilities for vision and social interaction (Tomasello), but there's such a hassle about that one tiny bit of possible innate language capabilities. So, why are all of those other innate capabilities acknowlegded so easily, why is language such an exception in being an ability that depends entirely on other innately dispositioned capabilities?

Second, CxG claims, that what appears as grammatical rules are abstractions over constructions. This view is problematic for cases that do not occur as part of the input. Here, Adger cites Yang (see answer from Mr. Hilbert), and he mentions the phenomenon of parasitic gaps: speakers of English have no problems in distinguishing between the grammatical and ungrammatical cases of parasitic gaps even though these kinds of structure are more or less non-existent in corpora. These structures can be captured by a a rules-type grammar, but how would a CxG-type analysis of parasitic gaps look like? From which kind of schemata are parasitic gaps abstractions? How can there be shemata for constructions that are not represented in the input?

So first, there is a problem in the premises, and second, there is a problem in descriptive adequacy or weak explanatory adequacy. The second problem could simply be addressed by just proposing how a CxG analysis of parasitic gaps would look like, but in her replies, Goldberg does not address the issue of how to analyse parasitic gaps.