Another question comes to mind. Hypothetically, what if a copyright holder simply didn't wish to have his song associated with a particular event, and refused permission for that reason? Does he have the right to control who can use his property in that circumstance?
But Limbaugh's show is obviously a commercial/for profit production so your question doesn't quite apply.
It used to be that 8 bars of a song could be used without royalties being sought, but I'm not sure if that's still law.