Finally, I'm struck that in this era of globalization, borders have disappeared for goods, for capital, for jobs... but not for people. Somehow, we have things wrong there. Either the borders become porous and rights become consistent or the borders should be more solid (I'll write more about this another day).
My hope is that all of the proposed solutions would come with a discussion that bettered them up...
And of course, there is also the scriptural injunctions regarding aliens, ie undocumented immigrants:
Leviticus 19:33-34 (NRSV)
When an alien resides with you in your land, you shall not oppress the alien.  The alien who resides with you shall be to you as the citizen among you; you shall love the alien as yourself, for you were aliens in the land of Egypt: I am the Lord your God.