Recent immigrants are a very small minority in the United States. The only reason they can affect the election is because approximately half of non-immigrants vote Democrat. They can be "the straw that broke the camel's back", but the straw can't break the back if the camel wasn't overloaded to begin with.
And by talking about non-whites vs whites you're confusing the issue. Hispanics whose family have lived in the United States longer than the United States has existed are far more American than European immigrants who came over last year.
Also, it takes a long time to get citizenship, so it's not like they're just came off the boat.