dick measuring contest
A conflict in which two parties (ususally male) are vehemently disputing something of limited relevance. Generally, both parties are somewhat wrong, but each refuses to be back down for fear of being thought the have the smaller of their two penises. Similar to a pissing match, but generally, the conflict involved involves a larger element of machismo, and  continues on only because neither side wants to be seen as the one who backs down.
The White House and the Conservative Right have been in a real dick measuring contest over the qualifications of this new Supreme Court apointee, Harriet Meiers.