hold out little, etc. hope

hold out hope

To maintain hope that something will happen or be the case, especially when it does not seem likely. Often used in negative constructions, and often used with modifiers like "much," "any," "little," etc., before the word "hope." We're still holding out hope that our missing son will be found. I know that this legislation is right for the country, but I hold out little hope that it will make it through both houses of congress. They didn't hold out much hope of being approved for a mortgage, given their credit history.
See also: hold, hope, out

hold out little, etc. ˈhope (of something/that...)

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not hold out any, much, etc. ˈhope

offer little, etc. reason for believing that something will happen: The doctors did not hold out much hope for her recovery.
See also: hold, hope, out