Here is the Libertarian position on immigration as revealed in their 2004 party platform which is almost word for word, their 1990 platform.
Immigration
The Issue: We welcome all refugees to our country and condemn the efforts of U.S. officials to create a new “Berlin Wall” which would keep them captive. We condemn the U.S. government’s policy of barring those refugees from our country and preventing Americans from assisting their passage to help them escape tyranny or improve their economic prospects.
The Principle: We hold that human rights should not be denied or abridged on the basis of nationality. Undocumented non-citizens should not be denied the fundamental freedom to labor and to move about unmolested. Furthermore, immigration must not be restricted for reasons of race, religion, political creed, age or sexual preference. We oppose government welfare and resettlement payments to non-citizens just as we oppose government welfare payments to all other persons.
Solutions: We condemn massive roundups of Hispanic Americans and others by the federal government in its hunt for individuals not possessing required government documents. We strongly oppose all measures that punish employers who hire undocumented workers. Such measures repress free enterprise, harass workers, and systematically discourage employers from hiring Hispanics.
Transitional Action: We call for the elimination of all restrictions on immigration, the abolition of the Immigration and Naturalization Service and the Border Patrol, and a declaration of full amnesty for all people who have entered the country illegally.
So what?
Not all libertarians are members of the Libertarian Party, much less support the Libertarian Party platform down to the letter and its entirety.
Just like not all conservatives are members of the Republican Party.
If you had bothered to read their platform completely, you'd have also seen this:
2.0 Economic Liberty A free and competitive market allocates resources in the most efficient manner. Each person has the right to offer goods and services to others on the free market. The only proper role of government in the economic realm is to protect property rights, adjudicate disputes, and provide a legal framework in which voluntary trade is protected. All efforts by government to redistribute wealth, or to control or manage trade, are improper in a free society.
Which would end our government's freebies to illegals, thereby eliminating the biggest reason that illegals have for coming here. As for the rest, I *WANT* those who would gladly work their butts off to make a better life to come to America.