Were there governments and laws set up that said that no other people besides Native Americans could occupy what is now America?
No.
And don't play the white people card. Illegal immigration isn't just non-white people, it includes white people who also cross the border illegally.
What people did 400 years ago who may or may not have even been our ancestors is completely irrelevant. Most did not break any laws in doing so, and if they did, it is completely irrelevant because we are not to be held responsible for what our "ancestors" did.
Also,
There are laws in this country and the penalties for breaking the laws should be enforced. If they are not, then what is the point of having them in the first place?
I'm not saying I support the way immigration is handled presently, but I do support the deportation of people who knowingly broke existing laws in order to gain entrance to the United States.