Instances of "close to the bone" in a literal sense go back at least as far as 1708. From the entry on "Bones" in John Harris, Lexicon Technicum: or An Universal English Dictionary of Arts and Sciences, second edition, volume 1 (1708):
The inner Superficies of the Periosteum sticks as close to the Bone as if it were glued to it ; and besides, the Periosteum has little Fibrillæ or Threads continued from it, that enter into the Substance of the Bone, which gives them (probably) some internal Sense.
And similarly, from Nathan Bailey, Dictionarium Rusticum, Urbanicum & Botanicum: or A Dictionary of Husbandry, Gardening, Trade, Commerce, and All Sorts of Country-Affairs, third edition, volume 1 (1726):
EXCRETION-BONEY ; an evil incident to Horses, occasion'd mostly by Causticks, or burning Corrosives, unduely put to Wounds that lie close to the Bone, as when the Wound is in the Leg, or about the Pasterns; for the Flesh being much burned by them, causes an Excrescence to grow upon the Bone, which by the little Experience of the Farrier is healed, but the Excretion remains; and sometimes it comes by a Shackle, or the galling of a Lock, or Fetters that have been long continued upon the Foot. What is proper for the Bone-Spavin, likewise cures this.
Figurative or poetic use "close to the bone" appears at least as early as Henry David Thoreau's poem "The Old Marlborough Road" (1850), reprinted in Collected Poems of Henry Thoreau (1943):
O man of wild habits, / Partridges and rabbits, / Who hast no cares / Only to set snares, / Who liv'st all alone, / Close to the bone, / And where life is sweetest / Constantly eatest.
From Oliver Wendell Holmes , "My Search for 'The Captain'" (1863), in Soundings from the Atlantic (1864):
A feeble, attenuated old man, who wore the Rebel uniform, if such it could be called, stood by without showing any sign of intelligence. It was cutting very close to the bone to carve such a shred of humanity from the body politic to make a soldier of.
And from Charles Van Zandt, "Commemorative Address Spoken Before the Rhode Island Society for the Encouragement of Domestic Industry" (January 19, 1870):
If you doubt this [the need for industry, intelligence, and morality in defense of Rhode Island's interest"] to-day, it will be irresistibly forced home upon you to-morrow, and you will learn how very close to the bone the unconscious tooth of humanity is always gnawing.
It is interesting that all three of the earliest examples of figurative use of "close to the bone" that I found are from New England sources. However, the number of instances is so small that it is impossible to draw any firm conclusion about the probable geographic origin of the phrase from those examples.
The origin of the phrase appears to be Old English: OED
to the bone or to the bare bone
- (a) to the bone (also to the bare bone).
- (i) Right through the flesh so as to reach the bone. Frequently hyperbolical, or in figurative contexts.
Old English usage:(prior to ~ 1300)
OE Ælfric Let. to Sigeweard (De Veteri et Novo Test.) (Laud) 61 On weallendum ele he het hine baðian, for ðan þe se hata ele gæð in to ðam bane.
And a more modern figurative uasge:
Swindells Follow Shadow (1991) I was walking head bowed and half blind in the teeth of a wind which keened like a mourner and cut me to the bone.
The phrase, in its current adjectival sense, seems relatively recent and of Scottish origins and found its way quickly into Modern English.
From the OED:
It seems to have started with
k. near (also close to) the bone.
(a) Scottish. Of a person or his or her behaviour: parsimonious; miserly, stingy.
1866 W. Gregor Dial. Banffshire (Philol. Soc.) 117 He's unco near the bane, wi' a' thing it he gees. [= He is remarkably near the bone, with anything that he gives]
1985 Conc. Sc. Dict. 436/1 Near the bane [=bone], miserly.
The idea of miserliness seems to have been associated with being thin because of a lack of nourishment – so miserly that a person would almost starve himself. It was then extended to include ‘having little or nothing’ and thus being dangerously close to disaster because of a lack of resources:
(b) Close to the minimum level or standard possible; esp. close to the limit of survival or subsistence; frequently in to live close to (also near) the bone: to live frugally or in poverty; to manage on the barest minimum.
1873 Milwaukee (Wisconsin) Sunday Sentinel 6 Apr. 6/2 He has had a hard time and has lived close to the bone.
2001 Technol. Rev. Dec. 87/2 Undoubtedly, many companies, running close to the bone, couldn't afford to safely clone their archives in more than one place.
In its turn, the meaning was extended again to encompass the meaning being generally in a dangerous position because of one’s own behaviour.
(c) Close to an established limit with regard to behaviour or politeness; verging on indecency or offensiveness; (also) uncomfortably close to the truth. Cf. near the knuckle at knuckle n. 2b.
1929 Smith's Weekly (Sydney) 29 June 14 Getting rather near the bone. After all, there are some things you simply can't make jokes about.
1980 Canberra Times 3 May 13/6 It is an utterly gripping story, but..too close to the bone, and too lacking in light relief.
2013 Daily Tel. 11 June 20/4 The self-mocking has to be close to the bone, it has to hurt, or it doesn't work.