"Chickenhawk" refers to those who strongly support the use of military force but avoided military service and combat themselves. It has nothing to do with a particular party.
And it is always used by people that have lost every other arguement on whatever conflict they are discussing. It is used as a last ditch effort to discount the opinions of those that they disagree with.
The premise put forth by the persons using the chickenhawk slur is that people that have not served in combat are not allowed to argue in favor of combat. Taking that to it's logical end, we could no longer elect a president that had not served in combat lest we not be able to defend ourselves if attacked.