I suggest you go to lp.org and read the Platform. There is a section covering "migration". Nowhere is Amnesty supported.
But, like most major political parties there is some disagreement on issues. For instance, the two most visable Libetarians, Judge Napolitano and John Stossel disagree on Abortion Rights. The party stance is that it is an individual's decision. However, what we do agree on is a limited Federal Government and a balanced budget among other issues!
3.4 Free Trade and Migration
We support the removal of governmental impediments to free trade. Political freedom and escape from tyranny demand that individuals not be unreasonably constrained by government in the crossing of political boundaries. Economic freedom demands the unrestricted movement of human as well as financial capital across national borders. However, we support control over the entry into our country of foreign nationals who pose a credible threat to security, health or property.
Hew, you are dodging the issue of Amnesty!
Again, nowhere does the Libertarian Party support Amnesty. Amnesty for millions of illegals is what the Dems are getting ready to present in thier bill. Amnesty would make them citizens of the USA with full benefits. We are against this!
Also, note the part about Free Trade. If the Libertarians get thier way, we won't be paying people to sit on thier poarches doing nothing. That woud drastically cut the number of illegals entering the country for work. If the illegals are willing to work for less, that would be a part of Free Trade. It would make our mfg. more competitve globally.
You have to look at the big picture!
We have an estimated 12million illegals here now. Tell me where the status quo of Bush's or Obama's policy has worked?