I believe that off-the-cuff, as in "off-the-cuff remark" for example, is a single word - a compound adjective, but I've got people claiming it is not a word at all, adjective or otherwise. Can you, please, please find a single grammarian, a single Anglophone even, who has supported the view of 'off-the-cuff' not being a single word?
"Off the cuff" cannot be thought of as a word in any grammatical context. As a syntactic constituent, this sequence of words is a prepositional phrase. As a PP it can be used as an attributive noun modifier, predicative complement or a manner adjunct.
He apologized for his off-the-cuff remark.
His remark was off the cuff.
The question cannot be answered off the cuff.
The fact that hyphens are used to set apart the individual words in the PP "off the cuff" functioning as an attributive noun modifier is quite understandable and is in no way peculiar to this prepositional phrase. As for the single authority coming from the Anglophone world who supports this view, I'll quote the Cambridge Grammar of the English Language. They deal with this question under chapter 20, "Punctuation", p1762, discussing the use of hyphens. Hyphens are divided into lexical and syntactic ones. The syntactic hyphen is used "to join into a single ORTHOGRAPHIC WORD sequences of two or more GRAMMATICAL WORDS functioning as attributive modifier in the structure of a nominal" Follows a list of phrases illustrating the use of syntactic hyphens.
Def1 "The hyphen explicitly indicates that the linked items form a constituent and hence may remove potential constituent structure ambiguities".
Def2 "The syntactic hyphen is used with expressions in modifier function that either do not occur elsewhere in the same grammatical form or occur elsewhere without hyphens"
If we accepted all hyphenated attributive expressions as words, we would run into two big problems. First, each of these words would need to be assigned to an existing or a new word class. (whether we opted for "adjectives" as the one or any other, that would make for a formally mind-bogglingly heterogeneous word class). Secondly, that would make the stock of words in English theoretically and factually infinite.
Now about classifying a prepositional phrase as an adjective. I strongly recommend you forget about thinking of one word class in terms of another. A prepositional phrase is a headed construction with a preposition as its head. An adjective refers to a word class that is identified as having a unique set of characteristics.
Compound adjectives are dealt with under a different chapter in CGEL, chapter 19 "Lexical word formation" Compound adjectives are a subgroup of the adjective class. It is a compound of two words, the second one being an adjective. I think that it is crystal-clear that "clear" and "crystal-clear" belong to the same class of words. (as is crystal-clear that "off the cuff" and "clear" do not)
Some compound words are hyphenated, some are not. The hyphen used to form another word is called a "lexical hyphen". Long story short, if a word is referred to as "a compound adjective", "a compound noun", "a compound verb", it has to have an adjective, noun, verb as the head. It is a good rule of thumb.
However, it is not invariably so. Section 4.3.3 p1660 of CGEL discusses the use of "..typically a nonce-form, typically restricted to attributive modifier function.". In expressions like "two-mile walk", "three-inch nail" etc., the modifier is a hyphenated word that does not "fit into the regular structures for these categories". "Two-mile" and "three-inch" do not qualify as nominals because their plural forms would be "two miles" and "three inches".
As the authors note under this section: "This is an area where it is difficult to draw a clear line between syntax and morphology" (allowing that these may be best treated as "compound adjectives", adjectives being the typical noun attribute). To see why "off-the-cuff" is unambiguously a PP, and doesn't have anything to do with compound adjectives (even these shady ones) refer again to Def2 above.
Hope that this will help you learn how to make a difference between the syntactically and lexically motivated uses of a hyphen.
I'll discuss the arguments in favor of adjectival analysis that Greg Lee offered in the post above.
PPs come after the noun they modify, not before.
Not only PPs but any possible form can be made a noun premodifier with the help of punctuation. I'll repeat that it is not only wrong to classify "off the cuff" as an adjective, even worse, it obscures what it is. There is an extremely productive process in noun premodification which allows creating a noun premodifier out of any syntactic form.
So recently when I was hooking up with this really sweet, but not-so-skilled guy, I decided to treat him to a dramatic performance.
Our A level student Mohamed Ahtash secured himself a once in a lifetime experience earlier this year when he was given the opportunity to fly to Morocco
“He didn't paint a glowing picture of himself, and he didn't have this 'I'm really cool' attitude.
The point is, punctuation included, a noun premodifier can be just about anything.
Also, if it were a PP, the object "the cuff" could be pronominalized, but *"I noticed my cuff was dirty, so I made an off it remark."
I don't think that this or similar syntactic operations on idiomatic expressions are possible in general, hence the term ïdiomatic. It is hard to even imagine the number of idioms that would be reclassified in all sorts of ways to accommodate this criteria. "Off the cuff"is a set phrase, it is an idiom that like other idiomatic expressions normally cannot undergo "a range of manipulation found with comparable free combination". The idiomatic status of the phrase, that is, its semantic interpretation, cannot be the sole criteria in the form categorization. In the literal sense, this phrase will be amenable to all sorts of transformation, including the one Greg Lee proposed.
like other adjectives, it can be modified by an adverb: "He made a very off-the-cuff remark."
As for "very" modifying the phrase, Ngram didn't return any results for "very off the cuff". A Google search for both "very much off the cuff" and "very off the cuff" returned a large number of results. To borrow Greg Lee's analysis here https://ell.stackexchange.com/questions/90779/is-very-much-an-adverb-or-an-adjective , "very much" modification precludes the adjectival analysis of the phrase "off the cuff" in the predicative position:
My remark was very much off the cuff.
This can be further corroborated by the analysis from CGEL p643 "A number of idiomatic PPs are gradable"(CGEL p643) - completely in control of the situation, wholly out of order, very much out of sorts etc. So, the phrase "off the cuff" belongs to a rather numerous group of idiomatiic PPs that can be graded. I'll take it that the PP analysis of "off the cuff" in the predicative position is unquestionable.
Even if we accept the "very" modification as a possibility, I don't see that this argument is strong enough as to warrant classifying what is quite strikingly a PP as an adjective. I don't see the point in saying that the PP "off the cuff" in "off the cuff remark" and "the remark is off the cuff" belongs to different formal categories.
Finally, this kind of analysis is not an isolated problem of course. Generally people try to find a perfect match between syntax and semantics. So in this case the reasoning is like, "something that describes something" has to be an adjective. But what if the form doesn't look like one? Well, let's make it an adjective anyway, it cannot be anything else. I guess that even now dictionaries label nouns as adjectives when they modify another noun. Seeking a perfect match between syntax and semantics is much like attempting to build a perpetuum mobile.
I agree that "off the cuff" is a word, and an adjective. PPs come after the noun they modify, not before. Also, if it were a PP, the object "the cuff" could be pronominalized, but *"I noticed my cuff was dirty, so I made an off it remark.", and like other adjectives, it can be modified by an adverb: "He made a very off-the-cuff remark."