I rather liked the way Quine described his contribution to empiricism in "Five Milestones of Empiricism" (p. 72 in "Theories and Things"):
The fourth move, to methodological monism, follows closely on this [Quine-Duhem] holism. Holism blurs the supposed contrast between the synthetic sentence, with its empirical content, and the analytic sentence, with its null content. The organizing role that was supposedly the role of analytic sentences is now seen as shared by sentences generally, and the empirical content that was supposedly peculiar to synthetic sentences is now seen as diffused throughout the system.
For some reason I like the phrase "methodological monism". I think it's the absence of any discussion of a method that does it for me.
I think this way of putting it makes the connection between the two parts of "Two Dogmas" clearer. The second dogma was being propped up by the first -- the dividing-up of empirical content among sentences was supposed to be handled by the analytic/synthetic distinction, with the analytic sentences providing a "framework" which could be filled in by the empirical content brought in by true synthetic sentences. Rejecting this picture (since the demarcation between framework and empirical content is arbitrary) leaves the analytic/synthetic distinction without any work to do; I take this to be why Quine says the two dogmas are "at root one".
Attempts to rehabilitate analyticity show up, in this light, as possibly being irrelevant to the "dogmas of empiricism"; analyticity which is insufficient to rehabilitate the organizing-organized dichotomy poses no threat to Quine's aims. (This would include Quine's own sense of analytic sentences in Roots of Reference, stipulative definitions, Strawson & Grice's insistence that we have at least a rough notion of analyticity on the grounds that there is in practice agreement on many cases, and McDowell's suggestion in the first afterword to Mind & World.)
(In case you were wondering, the other milestones are the shift from ideas to words, the shift from words to sentences, the shift from sentences to systems of sentences, and the abandonment of "first philosophy".)