Sounds like a variation on the Lincoln Douglas debate. I'll take Mr. Lincoln's position if you don't mind. :)
The founders were about natural law and natural rights. The point being, that no government had a right to infringe upon those. Among those rights were "Freedom of Speech, and Freedom of Religion, the right to self defense, the right to be free in ones person and effects...
What that means is there are those rights which are natural, and which are regarded as beyond the ability of the "state" to tamper with.
Natural born citizenship fits neatly into this category. If a person is born inside a nation's boundaries to two citizens of that nation, who can claim he is not a citizen?