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.
Why? If American Indians were capable to unite and push out the invaders/settlers when numbers were in their favor it would be OBJECTIVELY a smart and right thing to do.
Same with the later non Protestant immigration, limiting incomers to Protestants (with preference for the British) and relying on already high domestic birthrate would keep USA stronger and longer lasting.
Of course it would be much more boring place and we would not have Godfather movie, but you cannot have everything :(
Probably people like me would not be allowed in, but this should not cloud our judgment.
Do you want America to be a global market place without national identity to end up like Rome which fall apart into separate nations ruled by barbarian tribes?