It would appear that there is a significant disjuncture between GOP politicians and GOP voters. See an interesting analysis in the National Review based on Washington Post polling data published here.
The polling data says Republican voters believe the party is putting too little emphasis on illegal immigration, on Federal spending, and on the economy and jobs. Like the analyst for NR, I infer a connection in voters' minds between jobs and illegal immigration.
If Republican politicians cannot bring themselves to deal with these issues, interesting opportunities are created for independent candidates who are willing to do so.