c. 1300, "rough, shaggy, careworn" (originally of animals), from Old Norse rogg "shaggy tuft" (see rug). "The precise relationship to ragged is not quite clear, but the stem is no doubt ultimately the same" [OED]. Meaning "vigorous, strong, robust" is American English, by 1848.

We were challenged with a peace-time choice between the American system of rugged individualism and a European philosophy of diametrically opposed doctrines — doctrines of paternalism and state socialism. [Herbert Hoover, speech in New York, Oct. 22, 1928]

Hoover said the phrase was not his own, and it is attested from 1897, though not in a patriotic context. Related: Ruggedly; ruggedness.