Yeah, no kidding. They've been offered lots of ways of doing immigration reform and have zero interest. Also, they typically reject the idea of arresting and imprisoning the very top of companies that employ undocumented workers.
If they really meant what they say about how jobs are being "taken" from citizens, wouldn't they back such a thing? It'd be easy to shut down a lot of the employment of undocumented workers. Walk into Tyson or some other big company, arrest those at the very top (not low-level clerks; I'm talking C-suite people) and entertain the idea of REVOKING corporate charters of companies that do this.
All it would take is one extremely high-profile example and it would be a sea change. Do Republicans mean what they say, though? Of course not.