How can immigration affect America's identity or culture?

Immigration through the ages has affected American culture to the degree that most people are comfortable with food, music and religious beliefs from all over the world. The identity part has remained fairly static as most incoming groups have wanted to be American. Only since the 1980s have we experienced m migration by people who do not wish to be American, do not want citizenship and identify more as foreign nationals than aspiring US citizens. In my city the identity is strongly Mexican (even amongst US-born citizens) and becoming more so each day.