If the Republicans were smart, they would seal the border, take out the cartels, offer a path to some kind of foreign born "citizenship" ( or whatever name you want to call it - with heavy vetting, of course) to those who had no part in bringing themselves here, including mandatory service to the country in some form.
Any criminal behavior would revoke said "citizenship" as would any reliance on social services.
I know brilliant 20-somethings, illegals, brought here as babies - mathematicians, musicians with college degrees - who would be assetts to this country. It would be stupid to send them back when they've never known any other country and are completely assimilated.