I believe the whole debate is over the import of the word "sensible". Some folks fancy that permitting many (if not all) people currently in the U.S. illegally not only to have their presence regularized in some way, but essentially handed Green Cards after a little bureaucratic hassle and put on their way to becoming citizens, is sensible. Others think that tougher enforcement of existing immigration law, including quick deportation of anyone in the U.S. illegally is sensible.
I suspect what is really sensible is somewhere in between. (Personally I like "Red Card" proposals -- a way of granting permanent legal status to remain in the U.S. to some non-citizens that does not put them on a track to citizenship. We can quibble over who should be entitled to such status, but it blunts all the left's humanitarian arguments and would be a way of stopping chain-immigration through family reunion resulting in lots of new 'Rat voters.)
THE LIBERTARIAN POSITION:
COMPLETE PLATFORM TEXT
INDIVIDUAL RIGHTS AND CIVIL ORDER
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. governments 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.