First things first: do people really use it? Apparently they do. In the COCA, the frequency distribution looks like this:
Note that there are even some instances in newspapers and academic writing. And the usage seems to be picking up steam. Here's the frequency over the last 18 years.
The OED's earliest citation is from 1925, so it does seem to be an innovation, but based on what?
The pattern that jumps first to mind is a few + plural noun. But it's not exactly the same, and here we have to back up a few steps.
Quantificational nouns such as a lot, a bunch, and a majority are often followed by a prepositional phrase, headed by of, that the Cambridge Grammar of the English Language (CGEL) calls the oblique. For example, in the noun phrase a bunch of guys, the prepositional phrase of guys is the oblique. The oblique can be partitive or non-partitive. Where the reference is to a part of a larger group (e.g., a bunch of the guys) it is partitive but where the reference is to a whole group (e.g., a bunch of guys), it is non-partitive.
Here's how a few differs from a couple. You can have a few of the things (partitive) but not a few of things (non-partitive). Moreover, a few presents one more pattern: a few things (without of; a few is a dependent of things). This suggests that a few is not a quantificational noun at all, but rather a determinative (cf., many of the things, many things, & *many of things). To summarise:
|Partitive||a bunch of the guys||a few of the guys|
|Non-partitive||a bunch of guys||*a few of guys|
|Dependent (no of)||*a bunch guys||a few guys|
The question is, for those people, is the non-partitive construction also grammatical? It's so common that I imagine it must be, but I have no way of being sure.
Next, are there any other words that act like this? A dozen works very like few, as do numbers like hundred, thousand, million, etc. On the other hand, a myriad is exactly like a couple: for most people it's a quantificational noun, but for a few, it acts like a determinative. The following examples are from the OED.
1845 H. B. HIRST Poems 65 From every rocklet running, flow a myriad murmuring springs.Finally, I wonder what modifiers can work for each of these: a loud bunch of the guys, a very few of the words, a comparatively few people, a __ couple things, a __ myriad pieces of software.
1886W. W. STORY Fiammetta 189 The crickets were trilling a myriad infinitesimal bells in the grasses. 1915St. Nicholas June 709/2 There are a myriad worlds. 1955L. DE WOHL Spear (1957) III. vi. 220 There was a small thunderstorm..into which the people read a myriad signs and portents. 1981Harvard Jrnl. Asiatic Stud. 41 355 She would make me miserable a thousand, a myriad times. 1992N. STEPHENSON Snow Crash iii. 24 He is actually staring at the graphic representations..of a myriad different pieces of software.