Immigration policy is just another redistribution program. In the short run, it transfers wealth from one group (workers) to another (employers). Whether or not such transfers are desirable is one of the central questions in the immigration debate.
There is an isomorphism between immigration, outsourcing, and free trade in general. In each case, overall economic efficiency is increased, due to the law of comparative advantage. There are distributional effects, to be sure, but no nation has been able to demonstrate an ability to use trade restrictions of any sort to reduce overall poverty.
Redistribution implies that trade is a zero-sum game. Borjas implies that immigration works like a tax on low-income workers and a subsidy to high-income employers. Of course, in any sort of competitive market, employers do not profit from lower costs but must instead pass them onto consumers. But why let a little economics get in the way of a folk-Marxist story?
Immigration, like all other forms of trade, is positive-sum game. All forms of trade restrictions hurt the economy. Immigration restrictions may change the composition of the least-well off. Overall, however, by weakening the economy immigration restrictions are likely to produce more poverty rather than less.
I am not a passionate supporter of open immigration as an economic policy. I do not think that the gains are huge. But I am angry any time an economist misleadingly describes trade as a "redistribution program." At that point, you forfeit your identity as an economist and instead become a demagogue.
See also Daniel Drezner's take (note that Lawrence Katz, who co-authored a paper with Borjas, makes much more reasonable comments).