This term is something writers like Andrew Sullivan and Christopher Hitchens might use. It's not intended for general consumption but for the select few with the gastronomic tastebuds to appreciate its flavor in political discourse. Or so I surmise.
It would be fun to study this term from the point of view of an alien, and this is what I have done. The trick is to pretend that I don't know what decadent means (which turned out not to be much of a pretense at all), and to seek for its meaning in all the usual places.
I started with the Google. The impression Google gives on decadence is that it is a characteristic of kinky sex and chocolate gateaus. Only the third page gives a dictionary definition:
Noun 1. decadent - a person who has fallen into a decadent state (morally or artistically)
bad person - a person who does harm to others Adj. 1. decadent - marked by excessive self-indulgence and moral decay; "a decadent life of excessive money and no sense of responsibility"; "a group of effete self-professed intellectuals"
My Webster's Unabridged gives these synonyms for decadent:
corrupt, immoral, degenerate, debased, debauched, self-indulgent
It seems that the decadent left is an immoral, degenerate and debased left; that a decadent lefty is a person who does harm to others. This is strong language. But I doubt very much that most readers catch the intended meanings. The connections of decadence to chocolate cakes and exotic sex are just too strong in themselves.
When I see the term I think of old smoke-filled apartments with lofty ceilings and antique lace curtains covering the windows, Victorian furniture, bone-china tea cups erudite conversation carried out in languid voices. Perhaps there are small tarts with elaborate icing, expensive wine served in toothmugs, long rants about some revolutionary dead a hundred years. Somehow I can't imagine any kinky sex here but maybe I should try harder.
This may be an example of political sloganing where the framing has failed. Decadent sounds like a rather nice thing to be, on the whole, or at least an impotent thing as far as its politics are concerned. But more importantly, it makes me think of imaginary groups which have nothing to do with the real left.