We have our own horde of 3rd world migrants that don't view our country first. They're a higher percentage of our population. Furthermore, we're letting in 250k Muslims a year on top of our currently existing (and rising) 3rd world populace. We'll be in the same position, only with different groups. It'll be between us and Mexico instead, as the Mexican diaspora is (predominantly) loyal to their home country over the US.
We're the prototype for inviting 3rd world migrants in, Europe is who followed suit. Islam is just more noticeable, so the Europeans caught on quicker.