horns of a dilemma n. phr. Two choices possible in a situation in which neither is wanted. Usually used after "on". 
 Joe found himself on the horns of a dilemma; if he went to work, he'd miss seeing Mary; if he stayed out, he'd he too broke to take her anywhere.
 Joe found himself on the horns of a dilemma; if he went to work, he'd miss seeing Mary; if he stayed out, he'd he too broke to take her anywhere.  [TahlilGaran] English Idioms Dictionary ▲