Well, my claim is that with some effort we can be objective whether we our family was American for generations or we just landed here.
I think that any determination of "excessive" has to be subjective, whether our ancestors arrived in 1620 or last week.
"Excessive," to me, means "a level of immigration that is causing disruption to the population that's been here longer." I'm sure my husband's Cherokee ancestors thought that European immigration was excessive long before my Irish folks got off the boat in the early 1800's. And those Irish thought the arrival of Slavs, Eastern European Jews, and Italians was excessive.
And from their perspective, they were as "right" as one can be in a subjective judgment. Various waves of immigration did cause disruption to the earlier-arrived population, just as the influx of Mexicans is causing disruption today.
There is much, of course, that our government could do to discourage the influx and mitigate the disruption. However, they seem determined rather to encourage more immigration and to exacerbate the hostilities between the new arrivals and the present majority population.