Your ancestors were immigrants!
And your people are from...?
OK, yes, my ancestors came from somewhere other than North America. So did yours. So did everyone else's, in fact—including those of the Native Americans.
No matter where you live in the world you have an ancestor from somewhere else.
In other words, every nation is a "nation of immigrants;" the slogan is meaningless and certainly no basis for public policy.
That my ancestors were immigrants is irrelevant to the formation of a prudent public policy today; just because a policy was appropriate in the past does not mean it is necessarily eternally good.
If my ancestors were pioneers, am I constrained to advocate expansionism forever?