There is a fact we seem to agree on: there are at least a billion poor hungry people in the world. Another fact we may agree on: America has at least ten million illegal immigrants. We also have fairly liberal legal immigration laws under which over 2 million people arrive every year. The net result is that America has the largest percentage of foreign born in over a century.
There is no way of knowing how many of the world’s poor would make their way here if there were no laws restricting their numbers. Even if only 10% came, it would overwhelm our facilities and social safety net. I can’t give you evidence over what we would happen if we were to do something that stupid, any more than I can give you evidence of how much food would be left on the shelves of a grocery store if it opened its doors and declared all food was free. But we do have a history of millions of dirt poor people making their way to America even with existing immigration laws. You can’t prove with any evidence how many more will come if we throw the doors wide open.