A question related to open immigration policy

I appreciate the moral arguments for open immigration policy, and as an immigrant myself I'd like to see more people get the inestimable opportunity that my family and I have gotten. But at the same time, I'm daunted by some possible problems that open immigration policy might generate, and I thought I'd repeat a question that I blogged about in 2008 (stressing that it's just a question and not an answer).

Say that we consider largely removing limits on immigration, as was indeed the law throughout much of the nation's history. (Let's set aside narrow limits, such as on people with criminal records, terrorist connections, or easily communicable diseases.) Say also that we will offer these now largely legal immigrants those social welfare benefits that are in fact politically likely—not the bare minimum that some libertarians might like, nor the vast amount that some welfare-state proponents might suggest, but those benefits that are likely: Public education for their children, some level of health care, and the like.

Say also that we maintain the traditional liberties that we have long offered legal immigrants, such as the right to settle wherever they want (which likely means where they can find relatives, people from their home country, and jobs), rather than requiring them to stick to (say) South Dakota and avoid already crowded places like New York City or Southern California. And say that we likewise maintain the various traditional restraints that are in fact unlikely to be politically changed, such as imperfectly enforced minimum wage laws, imperfectly enforced tax laws, imperfectly enforced housing laws, and the like.

Of the world population of 7 billion, how many people are likely to want to come to the U.S., and stay for the indefinite future, under this model? Ten million? One hundred million? More? Less?

Relatedly, if one goal of allowing broader immigration would be to avoid the problems caused by illegal immigration, would capping the limit at some number (2 million per year? 5 million per year?) dramatically decrease illegal immigration by offering the prospect of legal immigration to those who stand in line? Or would it increase illegal immigration, as people see more of their acquaintances and family members living in the U.S., and thus conclude that moving here illegally would be easier and less painful than it once was?

Here's one data point I saw on this, back in 2008. The Reader's Digest reported the results of a poll that asked people in other countries, among other things, whether they "would be interested in moving to America if economic and political barriers were non-existent." (That's just the Digest's paraphrase, I should stress; please let me know if you know the exact text of the question, and more broadly whatever else you may know about the survey, since I recognize it might well be flawed.) The Digest gave answers for 17 countries, but let me just give the biggest one, India: 73%.

Now I strongly suspect that Indian immigrants to the U.S. have given the country a great deal, and that the country is on balance better for letting them in (as I hope is the case about Russian Empire immigrants like me). But, let me say again: 73%. Of over a billion people.

Naturally, economic barriers would never be nonexistent. But say that political barriers were removed, and only 10% of those people would actually come. That would be 80 million new Americans, perhaps in the span of only a few years. And that's just from India. Where would they all go? What freeways would they drive on?

Given this, would you have no immigration caps at all? If you would, how would you make the caps work?