Recent immigrants rarely vote Republican regardless of what Republicans do. Remember Sen Amnesty McCain didn't get many Hispanic votes either.
Actually immigration enforcement isn't that difficult, just be very strict with E-Verify.
And don't forget lower immigration BOTH legal and illegal would greatly benefit the country except for employers. When you consider employment, education and health costs, population congestion, terrorism, disease, language issues, use of govt services etc how can you not feel that way?
Don't believe ANY claim of labor shortage from employers. Why do H-1B, J-1, L-1 workers come overwhelmingly from low wage countries (forget Japan or Western Europe)? It's obviously about CHEAP LABOR these days!!