That's not actually true, though. Every immigrant who comes here and becomes employed is, of course, filling a slot that is no longer available to a native-born citizen. However, he or she will also be one more person who needs to be fed, clothed, housed, entertained, protected, and supported. All of those create demand that adds up to substantially more than one job (about 1.2, to be exact [1]).
If there's one thing I'm taking away from this campaign and election, it's that people have big problems reasoning about systems where costs are acute and centralized and benefits are diffuse, even if on the whole they personally benefit substantially from those systems. This seems true for immigration, for climate change, for free trade, for healthcare reform.