We must be careful before we idealize the past. It was World War II that assimilated the European ethnics, and made them realize they were Americans. Then came the red scare of post-WWII in which to be "foreign" was to be suspect. The "everyone wants to be American" concept is largely a product of postwar America.
In any event, it doesn't matter, every child of Colombian, Cuban, Cambodian, and Korean immigrants I have met speaks English better than their parent's language.
I'm fully aware that there as Hispanics, Asians, and others who are assimilating quite well into American society and wants to be American and I'm more than happy to have that sort of immigrant enter the United States. Regardless of where it started or how well it worked in the past in the United States, the "Melting Pot" was an admirable goal and far more sustainable than the multicultural ideals being preached by many academics. I'm by no means anti-immigration. I'm anti-multiculturalism to, the extent that many multiculturalists want to take it, and think America needs a single official language. If the people of India can understand the benefits of using English as an official language, despite it being almost nobody's native language in India, why can't Americans grasp the same benefits.
My grandfather, who is now in his mid 90s, came over to Jersey City from Eastern Europe when he was a young boy. If he'd stayed in Russia, his town would have been overrun within a week of Operation Barbarossa starting and he and his family would have been killed. Here, he raised a family and did very well for himself, growing up speaking English and working with all types of people.
You'd expect him to be as grateful to be an American as I am, given this record, but when I talked about it with him a few months ago he sounded like he was still a guest in this country and he didn't particularly feel like an American. Identifying with America, thinking about what it stands for etc. just wasn't relevant to him. Of course, he isn't Russian either, nor is he religious. He just is.