The proper response is to belittle this strategy. The GOP leadership ought to say something like this:
"Rush Limbaugh is not an elected official, nor a party leader. He's just a citizen with strong opinions who happens to be a talk show host. We find it rather sad that the president would choose to distract the voters from the real issues by attacking a citizen who has no formal position either in government or our party. In fact, we find it beneath the dignity of the office of the presidency."
After saying that, they ignore the attacks and never mention Limbaugh again, unless asked. If asked, they simply repeat that Limbaugh has no position within government or the party and that discussing him is distraction from the real issues.
Yes, yes, yes. Why is it that some guy posting on a web site in the middle of the day can understand this, but six and seven figure political consultants can't convince the GOP leadership and rank & file of the same.
NBC just released a new poll that has Dems winning the "economy debate" 48% to 20%. Why? Because our Republican representatives are too worried about defending Rush Limbaugh.