A significant thrust of the argumentation against Trump's immigration order is that it is in some sense un-American. Oddly the people asserting this are the same people who would tell you, accurately enough, that America has in the past responded exactly the same way to sharp spikes in immigration. This has been true from the Alien and Sedition Acts, to the Chinese Exclusion Acts, to FDR's ban on Germans and Japanese immigration (coupled with internment camps), one would think that this would properly be described as classically American. What they mean to say is that this isn't in accord with the America they want, even if it's an America that has never existed yet, but is hoped for maybe someday. This is mirrored by the occasional longing -- inherent in the cry to 'Make America Great Again' -- for an America that used to exist, but never really did.
My own sense is that America was always and is still the most immigrant-friendly nation on earth, a place where you can really become an American if you want to do so. The reason that there are periodic attempts to put the brakes on is not that America has shifted its core, but that assimilating new members of the society is an organic process that is governed by organic reactions.
You might say that, as a society, we get hungry, we gorge, and then we need to digest. It's a natural reaction by human beings to the introduction of a large amount of change and large number of strangers suddenly showing up in their lives. But it's not about ending immigration, even if that's the way people talk. It's a natural part of the process of handling immigration on the American scale. It may not be aesthetically pleasing to watch, but neither is digestion. Nevertheless, this is why America has been able to absorb all those waves of immigrants in the past, all of whose descendants are simply "Americans."
In any case, I would like to caution against either side presuming to speak for "America" on this point. Mr. Hines linked to a news story about this poll in a comments section below. A slight plurality favors Trump's order, 48/42. The recent election also went slightly for Trump, but only thanks to the Electoral College. Any Trump supporter has to take on board the fact that right at half of the country opposes him. Any Trump opponent has to take on board that right at half of the country supports him. The numbers may even be in flux, so that we can't say that it's a bit more than half for or a bit more than half against: it may be more one day than the next.
These visions of what America ought to look like, versus what it really does look like, are sharply divided. We should be cautious about painting as "un-American" the views of right at half the nation, whichever side we are on.