the earliest occurrence of to swap horses while crossing a stream
from The Pittsburgh Post (Pittsburgh, Pennsylvania) – 25^th September 1863

The phrase to change, or swap, horses in midstream, or while crossing a stream, means to change one’s ideas, plans, etc., in the middle of a project, progress, etc.

The locus classicus is a speech by the American Republican statesman Abraham Lincoln (1809-65), sixteenth president of the United States (1861-65), assassinated shortly after the end of the American Civil War (1861-65); on 9^th June 1864, he explained to a delegation from the National Union League that his renomination for President was due less to his own abilities than to the fact that his fellow Republicans did not want to take the risk of nominating a different candidate during the war:

from the Evening Star (Washington, D.C.) – 9^th June 1864:
Gentlemen, I can only say in response to the kind remarks of your chairman, as I suppose, that I am very grateful for the renewed confidence which has been accorded to me both by the Convention and by the National League. I am not insensible at all to the personal compliment there is in this, and yet I do not allow myself to believe that any but a small portion of it is to be appropriated as a personal compliment. That really the Convention and the Union League assembled with a higher view—that of taking care of the interests of the country for the present and the great future; and that the part I am entitled to appropriate as a compliment is only that part which I may lay hold of as being the opinion of the Convention and of the League—that I am not entirely unworthy to be intrusted with the place which I have occupied for the last three years. But 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 best man in America, but rather they have concluded that 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. [Laughter and applause.]

The day before, The Brooklyn Daily Eagle (Brooklyn, New York) reported that in a speech delivered the previous day at the first public political meeting of the Presidential campaign, held at the Republican Central Club of Brooklyn, Simeon Baldwin Chittenden (1814-89), who supported Abraham Lincoln, had declared that

Men outside of political influence, thoughtful men, believed it would be suicidal to change our chief ruler while the war continued—it was no time to swap horses while swimming the stream.

According to another report of the meeting, in the same edition of this newspaper, the phrase had been coined by Abraham Lincoln several months before:

Mr. Chittenden also told a little story, which has been familiar to us all for many months, as one of Mr. Lincoln’s best—it is about the man who declined swapping horses while crossing a river.

The phrase had indeed been “familiar […] for many months”, since, on 25^th September 1863, The Pittsburgh Post (Pittsburgh, Pennsylvania) invented a letter in which Abraham Lincoln uses it:

Mr. Thurlow Weed’s recent letter denouncing the draft leads people to say that it would not be strange if the next canvass should show to us Mr. Lincoln as well as Mr. Seward, as no friend of this unpopular measure. The chronicles of 1864 may present on this head some such letter from Mr. Lincoln as the following:
In regard to this draft business, people said to me that it had been very successful in other countries. France and Prussia, had raised excellent armies in that way. I replied that our fashion was to raise armies by voluntary enlistments. It was not a good thing to swap horses while crossing a stream. But it was urged that volunteering had ceased, and any horse was better than a dead horse. This does not strictly follow. The hide and shoes of a dead horse may be worth something. Moreover, the horse might not be dead, only perhaps shamming death, or in what the surgeon general, and that excellent institution the Sanitary Commission denominate a state of coma. Besides the new horse might be vicious. Certainly, from what is known of him, he requires expensive provender; then, if he should kick his owner’s brains out, better have kept the dead horse. Therefore I recur to my position, not to swap. But I signed the bill authorizing the draft. Of course, the President signs the bills passed by Congress, unless he vetoes them. I saw no occasion for a vote [misprint for veto]. The country was in a state of war. The men in Congress from the eastern states who voted for that bill, are supposed to have wanted a draft. They had it. The men from the western states who voted for it may not have wanted a draft. They did not have it. Anything will float where there is water enough. There seems to have been a drought in the western states that season, and only a heavy dew in New Jersey, as far as heard from.