The Republicans think they need to change their image
That's not the problem. Instead of trying to change how people perceive them, they need to change how they are. The other day Jeb Bush said, "We're associated with being anti-everything. Way too many people believe that Republicans are anti-immigrant, anti-woman, anti-science, anti-gay, anti-worker." Well, yes, Jeb, because you ARE. He left out "anti-environment" and "anti-not Christian." Probably an oversight; I imagine it can be hard to keep track of all the things you're against.
It's not just the messaging that's wrong, it's the fundamental, core, central, dear, lifelong, never-to-be-shaken beliefs of the people delivering the message. You can't just say "Hey, we're not bigots anymore!" You need to stop attracting bigots with all of the rhetoric that says "Hey, join us, we're the bigot party!" Birther? Join us! Tired of "them" (whoever your personal "them" happens to be)? Join us! Think any woman who speaks her mind is either a s-l-u-t, a lesbian or both? Join us!
They're not going to stop attracting bigots when they're constantly trotting out bigots to speak at their conventions and town halls. Donald Trump was a guest speaker just last week, as was Sarah Palin. Rush Limbaugh was made an honorary Congressman, for chrissakes.