Theodore Roosevelt's view of what it means to be an American

“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 person’s becoming in every facet 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… 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, 1907

You can see more details as to what he was thinking in the article Sole Loyalty where you get a much better idea as to what we an American should be doing today.