Well...the Indians also came from elsewhere originally...people don't grow out of the ground...so, essentially everyone, in every country is, by that definition, an immigrant or the descendant of an immigrant...and all nations are "Nations of Immigrants"...and, for that reason, no nation has any right but to admit immigrants...but I would say there is a difference between people who are colonists who's descendants later form a nation and people who are immigrants to an existing nation.
Ultimately, it should not matter whether your father or grandfather...or mine...was an immigrant...what may have been good policy for the US in 1907...may not be good policy in 2007...so I see no hypocrisy in saying that circumstances change and we no longer need immigration
Now...people may disagree...but to me, the only valid arguments for immigration are that "it would benefit the American people because [fill in the blank]"
Arguing that one supports immigration because their grandparents immigrated...or because it only seems fair...or because most Americans are descended from immigrants...those facts should be irrelevant to the only important question...would a particular immigration policy benefit Americans at this point in time?
I think no immigration is a mistake, pure and simple.