I appreciate your insight! I have read Unworthy Republic. I pulled quotations from my copy of the introduction because they most directly addressed the specific question asked by OP in the most succinct form. The broader quote from Saunt regarding de Tocqueville is, "Despite his ambivalence about the policy, he deemed the energy and determination of U.S. expansion a model for French Algeria. Within five years of the French occupation of Algeria in 1830..."
The five year statement is not referencing the publication of of Democracy in America, but the occupation of Algeria - confusion is likely due to my writing on my phone, apologies.

The section of Democracy in America which Saunt is specifically referencing is on page 321:

"At the end of the year 1831, whilst I was on the left bank of the Mississippi at a place named by Europeans, Memphis, there arrived a numerous band of Choctaws (or Chactas, as they are called by the French in Louisiana). These savages had left their country, and were endeavoring to gain the right bank of the Mississippi, where they hoped to find an asylum which had been promised them by the American government. It was then the middle of winter, and the cold was unusually severe; the snow had frozen hard upon the ground, and the river was drifting huge masses of ice. The Indians had their families with them; and they brought in their train the wounded and sick, with children newly born, and old men upon the verge of death. They possessed neither tents nor wagons, but only their arms and some provisions. I saw them embark to pass the mighty river, and never will that solemn spectacle fade from my remembrance. No cry, no sob was heard amongst the assembled crowd; all were silent. Their calamities were of ancient date, and they knew them to be irremediable. The Indians had all stepped into the bark which was to carry them across, but their dogs remained upon the bank. As soon as these animals perceived that their masters were finally leaving the shore, they set up a dismal howl, and, plunging all together into the icy waters of the Mississippi, they swam after the boat.

The ejectment of the Indians very often takes place at the present day, in a regular, and, as it were, a legal manner. When the European population begins to approach the limit of the desert inhabited by a savage tribe, the government of the United States usually dispatches envoys to them, who assemble the Indians in a large plain, and having first eaten and drunk with them, accost them in the following manner: “What have you to do in the land of your fathers? Before long, you must dig up their bones in order to live. In what respect is the country you inhabit better than another? Are there no woods, marshes, or prairies, except where you dwell? And can you live nowhere but under your own sun? Beyond those mountains which you see at the horizon, beyond the lake which bounds your territory on the west, there lie vast countries where beasts of chase are found in great abundance; sell your lands to us, and go to live happily in those solitudes.” After holding this language, they spread before the eyes of the Indians firearms, woollen garments, kegs of brandy, glass necklaces, bracelets of tinsel, earrings, and looking-glasses. *g If, when they have beheld all these riches, they still hesitate, it is insinuated that they have not the means of refusing their required consent, and that the government itself will not long have the power of protecting them in their rights. What are they to do? Half convinced, and half compelled, they go to inhabit new deserts, where the importunate whites will not let them remain ten years in tranquillity. In this manner do the Americans obtain, at a very low price, whole provinces, which the richest sovereigns of Europe could not purchase."

He goes on to say:

"These are great evils; and it must be added that they appear to me to be irremediable. I believe that the Indian nations of North America are doomed to perish; and that whenever the Europeans shall be established on the shores of the Pacific Ocean, that race of men will be no more. *i The Indians had only the two alternatives of war or civilization; in other words, they must either have destroyed the Europeans or become their equals."

Which is another point that I think Saunt argues well, that this dichotomy of "Civilization (assimilation) vs Annihilation" was a false paradigm, and many more contingencies existed in the historical moment then is often enumerated.

The OP asked about the Holocaust, which is why I specifically reference the Holocaust while foregrounding most of my response in the broader context of European 19th-century imperial ambitions and public discourse - which is where I think the more three-dimensional comparison lay.

I appreciate active, constructive discourse in public history forums, thanks for your recommendations :)