Like Geoff and Ben, I was puzzled by choice of "squeezed middle" as the OED's WOTY. But I agree with Ben that it's reasonable as well as traditional for dictionaries to include semi-compositional compounds and phrases among their entries. In such cases, a word-combination X Y has a common meaning that's an unpredictable specialization of its compositional meaning, so that you may not be able to figure out what X Y means, even in context, and you're even less likely to be able to guess that X Y is the term that you should use to convey the concept in question.
Thus the French noun remontée can be used to mean "rise" (e.g. of prices), "increase" (e.g. in violent incidents), "ascent" or "trip up" (e.g. of a river or a mountain), "recovery" (e.g. of the economy), etc. The phrase remontée mécanique is a normal NOUN+ADJECTIVE phrase, whose literal meaning is something like "mechanical rise" or "mechanical lift" — but its common meaning is apparently closer to "ski lift". From the compositional meaning of the phrase, you might think that it could be used to mean "elevator" or "escalator", but as far as I know this is unlikely at best.
There are also particular types of ski lift that may be named in French by complex words like téléski or compounds like tire-fesses ("pull-butt"). In all these cases, I know the meaning of the pieces and the general method of combination, and I could probably guess the meaning of combinations in a suitably redundant context. But out-of-context use could be confusing, and without relevant experience I certainly wouldn't know to use these combinations and not, say, ascenseur de ski. And the same sort of thing goes in reverse for the English phrases in the same semantic space, like chair lift, rope tow, J bar, and so on.
As for squeezed middle, there are at least three traditional circumstances in which this word-sequence is used: "squeezed middle children", "squeezed middle limb" (in geology), and, yes, "squeezed middle class". Some examples:
Frank Main, Perfect Parenting & Other Myths, 1986
[…] it is often the squeezed middle who presents problems. Middle children can smell injustice even if it's hermetically sealed with good intentions!
Maxine Marsolini, Blended Families, 2000
C. Lapworth, "The Secret of the Highlands", Geological Magazine 1883:
Herbert Bucksch, Worterbuch Geotechnik, 1998:
W.E.B. Du Bois, Dark Princess: a romance, 1928:
Robert Heilbroner, "The uncomfortable paradise of full employment", Harper's Magazine, April 1947:
The squeezed middle class (aided by the management class) will encourage anti-labor (really anti-wage) legislation in an effort to preserve its real share of the national income.
Harriet Bradley, Fractured identities: changing patterns of inequality, 1996:
During Bill Clinton's presidency there has been considerable talk of the 'squeezed middle', leading to consideration of tax changes which would benefit middle-class groupings.
There are many other applications of "squeezed middle" as well, with or without an explicit following noun — corsetting, hydrodynamics, earthquakes, whatever. Geoff's point is that the process of phrasal composition creates word-combinations with predictable meanings, which can then be used in indefinitely many particular circumstances. Ben's point is that linguistically-unpredictable cultural history often leads to some of these particular circumstances becoming a more-or-less established part of the phrase's meaning, which a lexicographer is then in duty bound to document.