That’s not what chicken hawk means. Broken pun.
It’s not a pun. The term has been used by both liberal and conservative press although with slightly different meanings. Thus the reason that the definition is at the top.
See examples below for use by both a well know conservative and liberal websites.
http://www.nationalreview.com/corner/247274/senator-feingold-deficit-chicken-hawk-cesar-conda
http://www.cepr.net/index.php/op-eds-&-columns/op-eds-&-columns/the-budget-deficit-chicken-hawks