Idiom or phrase about a situation in which a person has little hope

I think you are referring to the choice between the:

lesser of two evils:

• the less bad thing of a pair of bad things.

  • I didn't like either politician, so I voted for the lesser of two evils. Given the options of going out with someone I don't like and staying home and watching a boring television program, I chose the lesser of the two evils and watched television.

(McGraw-Hill Dictionary of American Idioms and Phrasal Verbs)

"between the devil and the deep blue sea" means between two dangers and by avoiding one there's danger of falling into another.

• from Wikipedia - "Between the devil and the deep blue sea" is an idiom meaning a dilemma—i.e., to choose between two undesirable situations (equivalent to "between a rock and a hard place").

• from TFD - if you are between the devil and the deep blue sea, you must choose between two equally unpleasant situations.

e.g.

• "If I pay the rent I won't have any money for food. I'm really between the devil and the deep blue sea."

• "For most people a visit to the dentist is like a choice between the devil and the deep blue sea - if you go you suffer, and if you don't go you suffer."