Robert Burns associated the fates of mice and men in his poem "To a Mouse" (1785):
The best-laid schemes o' mice an' men
Gang aft a-gley,
But this seems to suggest that mice and men have a lot in common. In contrast, the phrase "Are you a man or a mouse?" seems to invite the idea that mice and men are quite different. What is the origin of this phrase?
Best Answer
Antecedents: 'Are we not men?'
Questions along the lines of "Are you a man or a mouse?" or "Are we mice or men?" rarely appear in Google Books search results until the early twentieth century, but they have antecedents in rhetorical questions that go back much farther. Insistence on the special status of humankind is no doubt ancient, and rhetorical questions referring to that special status are quite old as well. For example, Fairburn's edition of The wonderful life and adventures of Three Fingered Jack, the Terror of Jamaica (1828) includes this outcry by Makro, a recently enslaved African, against slave markets:
The same notion is evident in The Merchant of Venice (by 1598), in the speech in which Shylock justifies his desire for revenge against Antonio:
In my view, this assertion of humanity (expressed as a rhetorical question) is one antecedent for the wording that the OP asks about. The longstanding, explicit contrast in idiomatic English speech and writing between mice and men is another.
Antecedents: 'a man or a mouse'
One of the links brought up by the search for the phrase "man or a mouse" cited in a comment by Hot Licks above is to this entry in James Halliwell, A Dictionary of Archaic and Provincial Words, Obsolete Phrases, Proverbs, and Ancient Customs, second edition, volume 2 (1852):
The Florio mentioned here is John Florio, who died in 1625, but who published a book titled First Fruits, which yield Familiar Speech, Merry Proverbs, Witty Sentences, and Golden Sayings in 1578. If that is the source of the phrase equating "a man or a mouse" with "something or nothing," then viewing the distinction between mouse and man as existentially crucial is very old indeed.
An echo of Florio's expression appears in a letter of May 1, 1712, from John Chamberlayne to William Nicolson reprinted in Letters on Various Subjects, Literary, Political, and Ecclesiastical, to and from William Nicolson, D.D. (1809):
The usage here is metaphorical, as what Chamberlayne is discussing is an event that may prove to be something or nothing. But the phrase could also be used in an either/or way to indicate the two prospects that lay before a young person. From Beaumont and Fletcher [maybe], Love's Cure, or The Martial Maid (by 1615):
Another early sense of "a man or a mouse" seems to be as part of an axiomatic test of ignorance, like the ability to distinguish a hawk from a handsaw, or an ass from an elbow. From a record of the trial of William Scot in 1612, reported in Richard Challoner, Memoirs of Missionary Priests, and Other Catholics of Both Sexes, That Have Suffered Death in England on Religious Accounts, from the Year 1577, to 1684 (1741):
But actions that prove one to be bold or timorous could also be expressed in such terms. From "Terry O'Daly's Visit to the Chateau D'Eu," in Bentley's Miscellany, volume 14 (1843):
Likewise the older distinction between significance (or worth) and insignificance (or worthlessness) remained in play in later years. For instance, from "Epigrams of Martial, Part 1, Translations, Imitations, &c." reprinted in The Wit's Miscellany (1774):
And from "The Resistless Foe," in The Anglo-American (December 6, 1845):
The dichotomy between boldness and timidity appears—again, not as a question, but as a choice—in Evelyn Benson, Ashcombe Churchyard (1861):
A review by John Manly of of Brandl's Quellen des weltlichen Dramas in England vor Shakespeare in The Journal of Germanic philology, volume 2, number 3 (1899) sums up the background on "a man or a mouse" as used in English:
Conclusion
It thus appears that explicitly asking a person whether he is a man or a mouse goes back at least as far as The Schole-house of Women, which was published as early as 1541, and is quoted by Hazlitt from editions drawn from 1560 and 1572. Nevertheless, the (almost) exact wording "Are you a man or a mouse?" doesn't appear in Google Book search results until a flurry of references to the following joke (taken here from The Literary Digest (May 13, 1905), which cites the Cleveland [Ohio] Ledger as its source:
And the first exact match for "Are you a man or a mouse?" appears in The Railway Maintenance of Way Employes Journal (September 1921):