I notice from your profile page that you are Catholic. Up until very recently, Catholics in this country were not considered "true" Americans, especially the Irish and Italians. It seems that the definition of who can be a "true" American has been malleable through history. Certainly, the idea that Blacks were true Americans would have been laughable up until very recently.
We therefore reject the idea that "we are a nation of immigrants" because our ancestors did not immigrate to a new country - they moved from one part of the Empire to another
Just to give you one example, over 40% of Americans have an ancestor who immigrated through Ellis Island alone. To claim that America is not a nation of immigrants is to defy reality.
But more fundementally, a nation by definition is people of common descent. If America is not a nation like Germany or Spain, then American is not a nation at all. Just a land with many different subnations. You are trying to redefine words.
You're using one possible definition, but another defintion, according to Webster's, is "a community of people composed of one or more nationalities and possessing a more or less defined territory and government; a territorial division containing a body of people of one or more nationalities and usually characterized by relatively large size and independent status." America fits either of those definitions quite well.
As to Anglo-Sexon dominance, that is still so. The majority of people in the US continue to report to the Census as being of ancestory coming from the original settlers of the US - from the British Isles, from Germany and Holland, from France, and from Scandanavia. The three largest groups are the Germans, English, and Irish.
Right there, your definition is too broad. You cannot honestly claim that the Irish would have been considered "real" Americans up until very recently. You pretty much have to exclude anyone who is of Irish (34 million), Italian (20 million), Hispanic (13% or so), Black (12%), Native (1.5%), Asian (1.2%), Jewish (2%), Muslim (1%) from the definition. That's nearly 50% of the country.
