With wordplay or misapprehension of the etymology: A faint hope, a ‘hope against hope’; an enterprise which has little chance of success.

= wishful thinking at wishful, adj. 2a(b).

In modern use in weaker sense: expressing or indicative of a wish; chiefly in wishful thinking, thinking, esp. belief or expectation, that is…

a wing and a prayer: a jocular form of reference (after quot. 1943) to an emergency landing by an aircraft; also figurative and as attributive.phr.…

objective, as straw-carrier, straw-clutching, straw-cutter, straw-cutting, etc.

to hope against hope: to hope where there are no reasonable grounds for doing so; to hope very much. Hence hope-against-hope.