The term IT MAY GO OUT ON A LIMB is a phrase that refers to taking a risk or making a bold statement. The crossword solutions for this phrase are NEST (4 letters) and TWIG (4 letters). A NEST is a structure built by birds, often made of twigs, which is a thin branch of a tree. Therefore, the two words together represent the idea of taking a risk and going out on a limb, as a bird would do when building its NEST.