This whole argument, whatever direction it goes in, will always end up back at illegal immigration, which is the source of probably 95% of the animosity on all sides.
That is really what Gingrich is railing against, and is why people will listen. Hell, I don't particularly like him (although he does write some pretty good
Civil War-based alternative historical fiction 
), and think how he said what he said is idiotic, but I do agree with the idea that giving benefits to people who literally break the first law of ours that they come into contact with by illegally crossing the border is a threat.
At least we can all agree that Newt really is one