Does anyone remember the name of a story and the author where the USA uses telepaths/telekinesis to prevent Russian nuclear bomb from detonating?
This happens in Robert Heinlein's 1953 short story Project Nightmare. The bombs are not dropped, but are smuggled into the US and hidden in various places. A team of psychics is used to locate the bombs and prevent them from exploding.
they don't get them all
Could this be Kurt Vonnegut's "The Report on the Barnhouse Effect"?
It features a professor who discovers telekinesis and becomes the first "weapon with a conscience", choosing to disable all weapons as soon as they're exposed. The story is told from the viewpoint of an ex-student who follows in his footsteps.
"Gentlemen," I read aloud, "As the first superweapon with a conscience, I am removing myself from your national defense stockpile. Setting a new precedent in the behavior of ordnance, I have humane reasons for going off. A. Barnhouse."
Another one is the novel Psychic Warrior by Bob Mayer and Robert Doherty. Published in 2000
Both US and Soviet use psychic warriors. The title matches the book, it is the primary theme of the book. Bombs are "launched" via psi as well as stopped via psi battle.