The Linguist List thread that @cori linked to has a couple discussions of what’s going on here. For example, one commenter says:
couple is coming into the English list of indefinite numbers,
just below few. … If
couple with this meaning is new in the language, I suspect that it
is picking up the grammar of the semantically adjacent word few.
I did a search in the Corpus of Historical American English for
A COUPLE OF [N*] and for
A COUPLE [N*], to search for incidences of these two idioms (
[N*] means some kind of noun).
From these results, we see that A COUPLE OF is much more common than A COUPLE, although it should be noted that there are incidences of
A COUPLE [N*] dating all the way back to 1820 in the corpus. Interestingly, both terms have been on the rise throughout the twentieth century, and the ratio between them has been decreasing, meaning that
A COUPLE [N*] is becoming relatively more common.