President Theodore Roosevelt’s view, 1903:

The mighty tide of immigration to our shore has brought in its train much of good and much of evil; and whether the good or evil shall predominate depends mainly on whether these newcomers do or do not throw themselves heartily into our national life, cease to be European and become Americans like the rest of us. More than a third of the people of the Northern states are of foreign birth or parentage. An immense number of them have become completely Americanized, and these stand on exactly the same plane as the descendants of any Puritan, Cavalier or Knickerbocker among us, and do their full and honourable share of the nation’s work. But where immigrants or the sons of immigrants do not heartily and in good faith throw in their lot with is, but cling to the speech, the customs, the ways of life, and the habits of thought of the old world which they have left, they thereby harm both themselves and us. If they remain alien elements, unassimilated, and with interests separate from ours, they are mere obstructions to the current of our national life, and, moreover, can get no good from it themselves. In fact, though we ourselves also suffer from their perversity, it is they who really suffer most. It is an immense benefit to the European immigrant to change him into an American citizen. To bear the name of American is to bear the most honorable of titles; and whoever does not so believe has no business to bear the name at all, and, if he comes from Europe, the sooner he goes back there the better. Besides, the man who does not become Americanized nevertheless fails to remain a European, and becomes nothing at all. The immigrant cannot possibly remain what he was, or continue to be a member of the Old-World society. If he tries to retain his old language, in a few generations it becomes a barbarous jargon; if he tries to retain his old customs and ways of life, in a few generations be becomes an uncouth boor. He has cut himself off from the Old World, and cannot retain his connections with it; and if he wishes ever to amount to anything he must throw himself heart and soul, and without reservation, into the new life to which he has come. It is urgently necessary to check and regulate our immigration by much more drastic laws than now exist; and this should be done both to keep our races which do not assimilate readily with our own, and unworthy individuals or all races—not only criminals, idiots and paupers, but anarchists of the…O’Donovan Rossa type.
…We freely extend the hand of welcome and of good-fellowship to every man, no matter what his creed or birthplace, who comes here honestly intent on becoming a good United States citizen like the rest of us; but we have a right and it is our duty to demand that he shall indeed become so, and shall not confuse the issues with which we are struggling by introducing among us Old-World quarrels and prejudices. There are certain ideas which he must give up. For instance, he must learn that American life is incompatible with any form of anarchy, or of any secret society having murder for its aim, whether at home or abroad… Moreover he must not bring in his Old-World religious race and national antipathies, but must merge them into love for our common country, and must take pride in the things which we can all take pride in… He must learn to celebrate Washington’s birthday, and the Fourth of July instead of St Patrick’s Day.