I feel that many of you are thinking of this immigration thing in a holdout neoconservative way instead of of applying true libertarian principles to the question.
In a true libertarian society, with no few if any involuntary safety nets, people aren't flocking in for a free ride. They come because of the promise of liberty and opportunity in exchange for hard work, talent and determination. In a true libertarian society, freedom of travel, both in and out is guaranteed. The government has no more authority to prevent you from buying land, settling somewhere, starting a business and being a productive member of society just because of who your parents were or where your mother went into labor.
The legitimate function of government in this case is to keep legitimate criminals and warmongers out, since a good defense prevents war and crime.
Of course, we don't have an ideal libertarian government now. Which is why wholesale elimination of immigration regulations is a bad idea right now. But how is it a bad idea to loosen immigration requirements for those immigrants that are productive, starting jobs or doing jobs that have demand for good workers, paying taxes, etc, and whose only crime is letting their visa expire or having the wrong visa (most "illegal immigrants" are visa overstays)? By all means, don't offer amnesty/citizenship to those who are a drain in the system, are criminals, etc. But it enhances the principle of freedom and promotes a free economy to allow all those who are participating in the economy to take a more active role, regardless of nationality.
And think of how it affects the liberty of american citizens, as well. Just like the TSA, the Customs and Immigration checkpoints are another place where US citizens and legal residents are harassed because of pointless rules. I've had several American, born and bred (white, european surnames for those prone to stereotype), harrased by passport control asking for a second form of identification other than passport -- the requirement for a state ID cannot be enforced by the federal government, in other words, trying to deny US citizens legitimate entry into the country. It is a crime to record, photograph or do anything of that sort during passport control and customs, another way which citizens are not allowed to avoid abuses while undergoing normal travel. Additionally, ever have a friendly "chat" with one of those officers in customs? They are recording everything you say, even if it has nothing to do with import duties, or your legal right to be in the country -- it is an excuse to ask you anything they want, with the threat of denying you entrance into your country of residence. Not to mention the fingerprinting and photographing of all legal permanent residents, and the RFID identification US citizens need to carry around as a result (I wouldn't be surprised if US citizens were fingerprinted as well, soon).
Some measures are necessary, sure, to avoid terrorism and what not. But do we really need to have such a state of treating citizens like criminals to deal with ordinary people traveling and living in the US?
It seems like the level of federal control over the whole system is counter to a libertarian philosophy. I agree thus with Sen. Rand Paul in: have legitimate border patrol and immigration controls to keep violence out of the system. But make it easier for everyone else, citizens included, to live and conduct business in the US, as the free market demands.