Immigrants are only going to stay in this country, if they can be successful here. For example, if they can open up a business and generate enough revenue to live a better life, or if they can find a job that affords them a better life than they had in their previous country.

Obviously, only a fool would stay here if their condition of living is worse here. If their life is worse here, they'll just move back! Duh! Immigration dropped sharply during the Great Recession, and large numbers of immigrants were actually leaving the country.

The one restriction I support personally is: No welfare or any kind of public support for immigrants. We don't want moochers. Also: don't allow them to sleep on the streets and stuff. We don't want the poor from the whole world flooding our streets, and asking for hand-outs. Kick them out. If someone can't be economically successful in this country, and make enough money to support themselves (i.e. through a job or a business), don't allow them to stay here. That's a reasonable restriction.

Economics will become a natural regulator of immigration. Those who can be successful here will stay. Those who can't will leave. I can predict that, under such welcoming immigration laws, the country's total GDP will grow massively.

On another note, people with facetious concerns about there only being a limited supply of jobs should read up on this: https://en.wikipedia.org/wiki/Lump_of_labour_fallacy

We had an insane level of immigration during the 1880-1921 period, and have we been poorer as a result for it? The US per capita GDP is exceeds that of most Western countries. (I guess one of the downsides is that NYC is now littered with pizza stores everywhere. Thanks Italian immigrants who flooded this country in the early 1900s!) This book covers this history in detail: https://amazon.com/gp/product/0809053446

I'm utterly and thoroughly opposed to those anti-free-market half-loosers who want to "protect" their jobs by preventing competition from others. This is just like the folks who want to require a license for everything, and want to use the power of the state (i.e. the threat of violence) to limit competition from others. With respect to immigration, I very reluctantly (partially) support mandating that immigrants be paid at least as much American workers, as this will prevent wage depression (even though this is an un-libertarian position). Our existing immigration laws already require this with every employment-based visa application. It's called the LCA (Labor Condition Application).

However, from a principled libertarian point of view, if another person else is willing to do your job for less money, well then, that's how much your work is worth. It's bad for society on the whole, for you to artificially inflate your pay grade by limiting the supply of available workers in your field.One of the reasons why medical costs are so high in the United States is that the supply of doctors is severely curtailed by regulation. It drives up cost for everyone, and it a net drag (or a tax) on the rest of people who need medical care. Government-imposed regulatory limits (on professional licensing, trade, immigration, the right to work, etc) protect various small interest groups at cost to everyone else, and are generally bad on the whole.