The suggestion that slavery in America would have lasted past the 19th century is ludicrous.
It was, in fact, a real possibility. Lincoln announced in his inaugural address that he would agree to the "Corwin Amendment." The Corwin Amendment would have made it virtually impossible to eliminate slavery before the 20th century.
No amendment shall be made to the Constitution which will authorize or give to Congress power to abolish or interfere, within any State, with the domestic institutions thereof, including that of persons held to labor or service by the laws of said State.
But this is a part of history that they refuse to tell people about.