Over time, that "otherness" has always baked itself into the fabric of our country over a couple generations, but there are some particular challenges for this wave. Mainly skin color and strong religious differences (for Muslims).
The whole "Spanish language everywhere!" problem is generational. First wave Italians didn't speak English either, but their children did.
So I think the anti-immigration vibe is nothing new and part of the process. Liberals might be making things harder by pushing for cultural preservation/independence rather than (through indifference) encouraging assimilation. I don't think supporting different cultures living side by side ever works out long term. If we either side can stop being so extreme in their approach, maybe we can continue our national process of assimilation and (begrudgedly) open arms to immigrants.