http://www.dailykos.com/storyonly/2010/8/22/895225/-The-blessings-of-liberty?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+dailykos%2Findex+%28Daily+Kos%29&utm_content=My+Yahoo"He has endeavored to prevent the population of these States; for that purpose, obstructing the laws for naturalization of foreigners,
refusing to pass others to encourage their migration hither."
--The Declaration of Independence
That was included among the principal grievances against George III enumerated in the Declaration of Independence. Both practical and principled men, they (the signers of the Declaration) recognized that the new country would have to be populated and they were anxious to attract large numbers of immigrants to this continent. The economic viability of the new country depended upon having a diverse and skilled populace.
On the principled side of things, they of course wanted to expand their vision of the blessings of liberty to all (propertied, white, male) persons of the world. Why shouldn't they? They were the beneficiaries of their forefathers (and mothers') ability to settle in this new land. Creating a new, flourishing democratic nation for the world to see and perhaps emulate meant not pulling the ladder of opportunity up after them.
But let's assume they took the attitude that the Dred Scott Republicans of today and would deny the benefits of citizenship to anyone whose parents weren't both born in the colonies. That would mean 22 of the 56 men who signed the Declaration, well, would probably have been denied that distinction.