When we say we don't have time to do something, it's one of the most standard euphemisms there is. And not having time sounds like a good xcuse. I usually use the word bandwith. It juss like i'm just so overwhelmed with all the things that i'm doing, but i would love to,. If i had the bandwith, i would, but i don't like this thing that you're asking me done. Doesn't sound like an idiotic thing, but i can't do it. No, absolutely not.
Also: what do you really mean when you say you “don’t have time”?