To run one’s face, or to travel on one’s face, is to live on credit. Goldsmith mentions “pushing a face” as one of the three ways of getting into debt. (N.E.D.)

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1856.  [I] must travel on my face after this when I want to go through the College.—Knick. Mag., xlviii. 504 (Nov.).

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1859.  If you have not a ready tongue, and cannot travel upon your face, you had better quit Macadam, and go to dwell in the unrestrained castle-building of your own heart.—Yale Lit. Mag., xxv. 60 (Nov.). (Italics in the original.)

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1862.  

        I ’ve hearn from ’sponsible men whose word wuz full ez good ’s their note,
Men thet can run their face for drinks, an’ keep a Sunday coat,
That they wuz all on ’em come down, an’ come down pooty fur,
From folks thet, ’thout their crowns wuz on, ou’ doors would n’ never stir.
Lowell, ‘Biglow Papers,’ 2nd Series, No. 3.    

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