Yes, indeed. It's fairly obvious.
In the case of illegal immigrants, however, the "GOP faithful" (the likes of Congressional leadership, Jeb Bush, McCain, Graham, Rubio, and so on) is barely distinguishable from the Democrats. Those groups practice obfuscation in the form of casting the issue one of "immigration" and xenophobia ignoring the "illegal" aspect; and "diversity" being something they want more of. Immigration is an issue that pits the elites against the workers.
The good news is truth is pulling our guys to the right. This issue works with the American people... and the left knows it.