What’s going to happen? Why did they say that? What does their resolution even mean? Check these choice excerpts from the Oxford English Dictionary.
1. With a singular or plural noun. Not any. (e.g., 1804 ‘E. DE ACTON’ Tale without Title: “I never reads no Novels; for I knows nothing they are good for.”) ...
6.b. Forming nouns with the sense ‘that is absent’, ‘that does not exist’, as no-confidence, -cover, etc. (e.g., 1948 D. BALLANTYNE Cunninghams: “Ralph showed off, riding no-hands and skidding in the loose metal.”)
1.a. intr. To be wanting or missing; to be deficient in quantity or degree. (1362 LANGL. P. Pl. A. v.: “And thauh my lyflode lakke letten I nulle That vche mon schal habben his.”)
2.a. trans. To be without, not to have; to have too little of; to be destitute of or deficient in. (e.g., 1813 SCOTT Rokeby: “I could have laughed—but lacked the time.”)
In conclusion, the Faculty “have too little” confidence in Summers, but not enough confidence in themselves to just say no.