Here is President Theodore Roosevelt's view of immigrants and assimilation:
"In the first place we should insist that if the immigrant who comes here in good faith becomes an American and assimilates himself to us, he shall be treated on an exact equality with everyone else, for it is an outrage to discriminate against any such man because of creed, or birthplace, or origin. But this is predicated upon the man's becoming in very fact an American, and nothing but an American ... There can be no divided allegiance here. Any man who says he is an American, but something else also, isn't an American at all. We have room for but one flag, the American flag, and this excludes the red flag, which symbolizes all wars against liberty and civilization, just as much as it excludes any foreign flag of a nation to which we are hostile ... We have room for but one language here, and that is the English language ... and we have room for but one sole loyalty and that is a loyalty to the American people."
—Theodore Roosevelt, 1919
I suspect that the immigrants may have shared the President's view, as my grandmothers, who came to America from Eastern Europe during the first decade of the 20th century, spoke only English in my presence, their children only learned English, they were intensely proud to be Americans, and (surprising to me in retrospect) my grandmothers never once even mentioned their childhoods in the old country.