The strongest argument against free immigration, from the standpoint of supporters of the free market, is that immigrants from poor countries may come not in order to work but in order to take advantage of a rich country's welfare system. Seen from one side it is an argument against free migration, seen from the other an argument against a welfare system. The easier it is for poor people to come to take advantage of welfare, the less attractive redistribution looks to the taxpayers paying for it, hence the less generous the system is likely to be. That may explain why levels of redistribution are generally lower in the U.S., where welfare was traditionally handled at the state level and intrastate migration was free, than in Europe, where welfare was handled at the national level and interstate migration was restricted.
Was. Within the E.U., there is now free migration. That puts pressure on national welfare systems either to reduce the level of transfers or raise redistribution to the supranational level. That pressure was limited as long as all E.U. members were relatively wealthy countries, became greater with the admission of poorer members from eastern Europe.
It is now greater still as the willingness of some European states to accept refugees and treat them generously, combined with conflicts that produce large numbers of actual refugees while making it difficult to distinguish them from voluntary migrants, is creating a flood tide of would-be residents on Europe's southern and eastern borders
One way in which the E.U. might respond is by restricting immigration. That will be difficult when many of the would-be immigrants are fleeing real dangers, hence natural objects of sympathy. How do you distinguish real refugees from migrants seeking to take advantage of generous transfers (330 € monthly, accommodation, language courses and so on during the six months that it takes Germany to decide whether or not someone qualifies for asylum, according to a comment on a recent post here)? And immigration restriction is made more difficult by the fact that border control is done at the national level. A country with low levels of redistribution can leave its border open in the expectation that most new arrivals will promptly depart for richer fields.
An alternative is to offer asylum on terms sufficiently unattractive so that only those fleeing real dangers will be inclined to take them—no welfare payments for five years, the current Czech policy for non-asylum migrants. That is the immigration policy that I recommended for the U.S., along with open borders, more than forty years ago in the first edition of The Machinery of Freedom.
Either policy might solve the immediate problem but still leave a situation where rich E.U. nations with generous welfare policies can expect to attract poor people from poorer parts of the E.U.—who, under current law, have the same rights as existing residents. It will be interesting to see whether the result is to shrink the European welfare states or to shift redistribution one level up, converting the E.U. into something a little closer to a United Statues of Europe.
For those in favor of free immigration and opposed to redistribution, the optimum solution, within the E.U. and in the world more generally, is easy. Arguably, the same solution should be optimal for those who support redistribution for egalitarian motives. Open borders plus the abolition of transfer payments might increase inequality in the U.S. or Germany but would surely reduce inequality on a global scale, the poor of India and Egypt, who would benefit, being much poorer than the poor of the U.S. or Germany.