The National Football League is widely recognized for having the smartest executives and the shrewdest owners in sports. But as the clock ticks down toward another deadline in the ongoing labor talks, that reputation may be called in for review.

The league's precarious position in these talks is a frustrating development for an institution that has always prided itself on internal stability. With the current collective bargaining agreement with the union set to expire at 12:01 a.m. on Saturday, the NFL faces several tough...