If the song has fallen into the arena of “public domain” or if the RNC or McCain/Palin campaigns subscribe to ASCAP or BMC(?), they don’t have to have permission.
Public domain songs are those whose copyright of 7 years has expired and may be freely used by anyone.
ASCAP and BMC(? I can’t remember if it is BMC or BMA), subscribers pay royalties to the artists during the time that the copyright is active. As long as the copyright is active or renewed, the artist(s) or the publisher can control who can use their music under which circumstances.
Song copywrites depend on when it was published. Music pubished before 1978 has a 95 year copyright. Music published after 1978 has a copyright of the life of the oldest surviving author plus 70 years. Anything published before 1923 in in the public domain.