Victoria Nuland, the woman who was caught on the leaked tape saying "F*ck the EU", essentially because the EU was not quite as enthusiastic about supporting further action, was the principal deputy foreign policy adviser to Vice President Dick Cheney.

http://en.wikipedia.org/wiki/Victoria_Nuland

Obama has a lot of stuff he has to deal with on a daily basis - listening to the audio, it would make sense that she is calling the shots on a daily basis. you can hear her saying that she is going to arrange biden to give an "attaboy" which is basically "i need a guy in a leadership role to appear to bless this" not that biden is actually making any substantive decisions.

https://www.youtube.com/watch?v=CL_GShyGv3o

Her brother-in-law came up with Bush's "surge" strategy in 2007, her husband was a foreign policy advisor to mccain in 2008. i would guess that's not the full extent of their republican advisory work but that's all i found in a minute or two on wikipedia.