Those who think low-wage immigrants hurt the economy are economic illiterates. They are falling for the fallacies of protectionism. The country as a whole does not benefit from "high wages" maintained by excluding low-wage immigrants, just as the economy as a whole does not benefit from any other form of protectionism. People are made wealthy by PRODUCTION of actual goods and services.
The REAL reason to keep illegal immigrants out is to preserve the culture and national sovereignty of the United States. There may be an economic COST to doing so. But it's still worth doing.