It might feel short-term good to have someone say yes, but when they don’t fulfill their agreement that leaves a more long-term feeling that their answers in the future will be unreliable (“Yeah, X told me they’ll do it soon, we’ll see if they actually do…”).

Communicating honestly (“If we need that done today, we have to deprioritize something else to make time”) will get you further unless you’re dealing with very immature management.