King Alfred pointed me to this post which examines the grammatical status of such phrases as "butt-crack of dawn." He sides with one Prof. Pullum as opposed to one Prof. Liberman in calling the phrase as a whole a "folk metaphor" as opposed to seeing "butt" as an intensifier.
Some time ago I considered phrases such as these and came up what I called the "Law of Vulgarization" in order to explain them. The Law of Vulgarization states that any syntatically correct phrase or statement may be made more emphatic by the substitution of one or more of its words: a vulgar word for a non-vulgar word. The new vulgar word need not make sense in the context, and the resulting phrase or sentence need not make logical sense in its new form: it derives its sense from its previous, implied form and its new degree of intensity from the degree of vulgarity of the substituted word.
The particular phrase which occasioned the creation of this law is a good example: I was asked to explain the derivation of the phrase "half-assed". After some thought, I concluded that the phrase could only be a modification of the phrase "half-hearted". Now, saying that something was done "half-hearted"ly makes sense: the heart is considered the seat of desire, so that to do something with half your heart is to do something with less than full desire to see the deed done. But saying that something is done with half an ass just makes no sense. It was clear to me that the sense was the same, however, but that "half-assed" is a bit more emphatic: more typically used when angry or frustrated at the performance of a job.
Now, I think this phenomenon is similar to "metaphor", in that a certain stylistic flair is often evident in the choice of the substituted word: "butt-crack of dawn" is a good example of that, connecting the unpleasantness of a time with the unpleasantness of a thing, and thus evoking resonances with the phrase "a shitty time of day". But I think, overall, that intensification is really the name of game, given many examples where any real meaning conveyed by the new word is absent. For example (and this was another one of my favorites, spontaneously created by a friend of mine): "everyone and his butt is going to be there." This is obviously redundant, since one would expect everyone coming "there" to also bring their butt. Further, this redundancy actually works against the logic of the original metaphor, "everyone and his brother will be there", in which it is important that one would not expect more people beyond "everyone" to be "there", but that more people (the "brothers") will in fact be there. So, changing "brother" to "butt" and hence, in strict logic, reducing the number of people implied to be "there", one, in simple logic, reduces the effect of the phrase. But in fact, by the Law of Vulgarization, the substitution in fact adds emphasis rather than subtracting it, as the meaning of the word "butt" in the new context is unimportant.
Note that this example also illustrates a corollary of the Law, which is that since the fact that the sense of the transformed phrase comes from an implied previous phrase, the implied previous phrase should still be fairly obvious after the substitution. Hence, you will most often find the Law in operation on fairly common stock phrases.
Now, why does vulgarizing a phrase make it more emphatic? This is easily enough understood. Vulgar words, by definition, have polite societal restrictions on use. The use of such words, therefore, often (if not always) implies a degree of emotion on the part of the speaker: a certain state in which the speaker is not inclined to care about societal niceties. Hence, the natural and spontaneous use of these words as intensifiers is perfectly understandable.