E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
To row up Salt River. A defeated political party is said to be rowed up Salt River, and those who attempt to uphold the party have the task of rowing up this ungracious stream. J. Inman says the allusion is to a small stream in Kentucky, the passage of which is rendered both difficult and dangerous by shallows, bars, and an extremely tortuous channel.