The homely American phrase “to swap horses in midstream” is just our way of saying “to change leaders (generals, presidents, or what have you) during the course of an engagement (or at the height of a crisis),” and the point is always stressed that such change may lead to disaster.
As a matter of literary record, Abraham Lincoln is credited with the utterance, though one historian of that period said that Lincoln quoted an old Dutch farmer, and Mencken reports the occurrence of the phrase some twenty-four years before Lincoln used it.
The occasion of Lincoln’s use was an informal address that he made to a delegation from the National Union League who had called to offer their congratulations upon his renomination for the presidency, June 9, 1864.
Lincoln knew that there had been considerable disaffection with the conduct of the Civil War and that many loyal Republicans felt that he had failed as the commander in chief.
Hence, in his speech, he said, “I do not allow myself to suppose that either the Convention or the League have concluded to decide that I am either the greatest or the best man in America, but rather they have concluded it is not best to swap horses while crossing the river, and have further concluded that I am not so poor a horse that they might not make a botch of it in trying to swap.”