Normally pure libertarians are for 100% open borders and for firing the Border Patrol and INS, it is in the libertarian party platform.
The bottom line is that they are not that different...
Ted Cruz Speech Nods to Increasing Libertarian Views within Republican Party
http://www.cato.org/blog/ted-cruz-speech-nods-increasing-libertarian-views-within-republican-party
GOP Congressman: Cruz Is A Libertarian, Not A Mainstream Republican
Ted Cruz: Libertarians Should Be Dismayed By Obamas Selective Enforcement Of Drug Law
Ronald Reagan’s opinion on Libertarianism
http://www.youtube.com/watch?v=Dg0Axyvlkm0