The found fathers listed immigration restrictions as a grievance against the King George in the Declaration of Independence. They wanted open borders.

“He has endeavoured to prevent the population of these States; for that purpose obstructing the Laws for Naturalization of Foreigners; refusing to pass others to encourage their migrations hither, and raising the conditions of new Appropriations of Lands.”

Someone pointed out to me that this isn’t necessarily saying they wanted open borders, just that they didn’t like the British hindering immigration; maybe they just wanted to limit immigration as they saw fit. I would agree that it’s not giving a lot of detail on what they wanted, but we can see what they wanted after they came to power. Not only did they keep the borders wide open, but they didn’t even give the federal government the power to regulate immigration in the Constitution. The U.S. had open borders until the Chinese Exclusion Act of 1882, and almost completely open borders until the 1920s, and open enough for most people to come in even until 9/11.