We have never been a melting pot. Blacks, American Indians, and Mexican-Americans remain distinct racial groups. Until recently, even WHITE people were segregated (Anglo, Italian, Jewish). The whole "melting pot" concept was socialist anyway ("all united in the class struggle) and an INVENTION of early 20th century propaganda.
The concept of there being races of humans (in the modern sense of race) is a socio-cultural construct, not strongly based upon science or genetics. Americans can be simply Americans. Some can be of a dark complexion with a tight, curly 'fro; some can be of a pale complexion with round eyes; some can have slanted eyes, etc. There CAN be one American race (using the old sense of race as nationality or ethnicity (grouping people based on a common culture)).