Although I think they were developed independently, "chattering class" is reminscent of a much earlier phrase used by a nineteenth-century Spanish intellectual called Juan Donoso Cortés. Cortés called the liberal bourgeoisie "una clasa discutidora", a term he meant with derision. Understanding him allows us to see more clearly the insult intended in the term "chattering class".
Cortés was a Catholic who lived in a time when the influence of liberalism was growing. He believed in moral absolutes, rights and wrongs. What hence struck him about political liberalism was the way that it had no absolute beliefs beyond a demand for constant rational discussion. He saw in this a strange emptiness and even a cowardliness, the former because it was as if the liberal believed in nothing beyond the discussion itself, and the latter because the liberal was hence disowning responsibility for the action which followed the discussion.
With his belief in moral absolutes, he believed instead in a philosophy of action: that what mattered was not the discussion, but what one actually did. Having absolute beliefs which liberalism did not and could not acknowledge, he saw no point in discussion with liberals. Either God is or is not sovereign on earth; there is no compromise between these two positions.
This complaint also lies in the meaning of "the chattering class". Marxists, fascists, the religious, or plain old conservatives often feel derision towards the "chattering class", who appear alien to those who have strong beliefs that they consider beyond debate. It was partially in reaction to this liberal tendency for temporizing that Nazism and Communism developed with their cult of irrational action: nor are we free of such movements today. Liberal politics must be effective as well as thoughtful to avoid their lure.