Although you asked for a proverb or expression (which simchona has provided), there's also a single word for this: a dilemma is a choice between equally unappealing options. From the Oxford English Dictionary:
1. In Rhetoric. A form of argument involving an adversary in the choice of two (or, loosely, more) alternatives, either of which is (or appears) equally unfavourable to him. (The alternatives are commonly spoken of as the ‘horns’ of the dilemma.) Hence in Logic, a hypothetical syllogism having a conjunctive or ‘conditional’ major premiss and a disjunctive minor (or, one premiss conjunctive and the other disjunctive).
2. Hence, in popular use: A choice between two (or, loosely, several) alternatives, which are or appear equally unfavourable; a position of doubt or perplexity, a ‘fix’.
One of the example sentences is:
1888 J. Bryce Amer. Commonw. II. liii. 332 They were‥in the dilemma of either violating the Constitution or losing a golden opportunity.