What is true is that making illegal immigration a signature issue does not seem to round up many swing voters. I don't think the issue caused many votes to switch either way in either the 5th or 8th district in Arizona.
States like NH may already be gone, and Colorado, Arizona and Nevada are showing signs of slipping away because of these issues. Moderates are souring on the Republican Party because of perception issues. I recall "back in the day" when a Republican could easily win a California Congressional district that had a 10% Democrat registration edge because the Pubbie would get the indies and get a large Dem crossover vote. No longer.