Now a question for you, do you really care anything about stemming the flow of immigrants or are you also for “free and open borders” like the Libertarian position paper advocates?
I'm against all illegal immigration, and believe our government has been derelict in its duties to secure our borders and enforce the existing laws. I know that fences alone are purely symbolic, and an array of surveillance devices combined with real border patrol enforcement is the minimum required to secure the land borders of our nation. Penalties for illegal border crossing should be increased, including jail time before deportation, and violators should be prosecuted to the full extent of the law.
I am in favor of reasonable amounts of legal immigration of individuals who have met a set of requirements related to their ability to contribute to the growth of our country, their willingness to forgo government benefits, and background checks related to their character and security concerns. Many of these requirements exist today. They should be strengthened, and people from areas of the world where anti-American sentiments are common should face very thorough scrutiny.
Historically, our nation has not had numerical limits on immigration for a large part of its history, but during those times there were essentially no ongoing government benefit programs. At this time the political character of our nation is such that it is very unlikely that the public would support no government benefits at all for immigrants, or other options such as increased taxes for immigrants, or very stringent earnings and/or wealth requirements, that would limit the inflow of immigrants without actual numerical quotas. So at this time quotas seem necessary. In general I think raising the requirements for immigrants is a better approach than quotas if possible.
There is no necessary reason that individuals granted visas to enter our nation to work have to be granted any path to citizenship (or any particular government benefits), although they should not necessarily be forbidden to seek citizenship. It would benefit our country to have less micro-management of the visa process for individuals coming to our nation to work, and to streamline that process and make it more widely available. Right now we have separate categories for fashion models, athletes, scientists, etc. with way more red tape than is necessary. A simple process to admit individuals to our country to work, without eligibility for any government benefits, but with comprehensive security checks would be a good idea. This however does not imply I would support unlimited numbers of this type of visa.
I do not think it is advisable that the children of non-citizens born in our country be automatically granted citizenship, or that non-citizens present in our country are offered any more than some minimum set of government services, akin to what most countries offer to non-citizens. For example, just about every civilized nation provides emergency services to citizens and non-citizens alike -- if you get hit by a car crossing the street in Korea they'll get you to a hospital whether or not you are a citizen. But paying for the bill is up to you, not the country you are visiting. We should do the same thing here.
Summary -- illegal immigration must be stopped, our border secured, and the immigration laws enforced. Legal immigration, whether for individuals coming to our nation to work or invest in businesses for a period of time, or for people who desire to become productive, patriotic Americans is a good thing. But non-citizens in our country should not expect nor receive the benefits citizens do.
After reading your post, I can only conclude that your not a Libertarian. In fact, I have no real disagreements with your positions. Although, I would add a few points.
There are other problems besides public acceptance for treating immigrants differently than natural born citizens. First and foremost, I doubt they would survive a legal challenge on equal protection grounds.