Although immigration can be of great benefit to societies, when it goes wrong -- such as illegal immigration, or when incomers cannot find work, or when new citizens refuse to adapt to the societies they enter -- the benefits are eroded and the native population starts to resent the people it had originally invited to join them.
The United States seems to have done a good job on integrating its immigrants, to the point where its many groups have made such wonderful contributions to life in their new country that it is hard to see what America would be without them. Although, as Moynihan and Glazer revealed in Beyond the Melting Pot, the pot never completely melts, the Poles have learned to speak English; they pledge allegiance to the flag and they serve -- and die -- in the military. But they still eat pierogi, attend mass in a Polish church, play Polish music (however corrupted) and preserve memories of their grandmothers and grandfathers. To them, the future is American, and tastes of pierogi, kiełbasa, and hamburgers.
The situation in Europe, particularly here the United Kingdom, is not so rosy. We have a largely positive history of deserving migrants wending their way to our shores. Huguenots, Jews, Hong Kong Chinese and others have all contributed well to these islands -- although the Jews have often been treated badly in return. During and after the Holocaust, Britain let very few Jewish refugees from Germany and Eastern Europe enter the country; blocked many thousands from travelling to Mandatory Palestine, and put many more thousands on Cyprus, where they lived under harsh conditions, hemmed in by barbed wire in detention camps.