I have tons of time. And while right now is a very slow time for me, very rarely am I so very super busy, and even then, I could usually make time if I valued something. Since I am fully aware of this, I don't think I often (if ever?) say that I don't have time for something.
However, I am often asked to do lots of things that I just don't value enough to priortize, which I often turn down. I usually respond with something along the lines of how important X is for Y reasons (assuming I can come up with some that I genuinely believe), but unfortunately I am just not able to commit to it right now. Sometimes I may mention other things that I'm doing if I believe that I am really already fulfilling my obligations doing related things (so if asked to serve on X committee, I might say that I'm not able to b/c I'm on Y and Z committees).
So, my responses may imply that I don't have time, but I don't often say this directly, b/c frankly, I don't feel honest in doing so. I try to walk the line between telling the truth but not volunteering info that's not someone else's business. And if I feel like I'm fulfilling an obligation of my job (eg, already serving on enough committees), then I don't feel obligated to do more just b/c I "have time," and will use what I'm already doing as part of the reason I'm saying "no," although it might imply to others a lack of time.
What I find interesting are all the people I know who have the same job that I do, do a much worse job at it (eg., get way less done in very tangible ways), but are always complaining about how little time they have. While I think that perhaps sometimes they are trying to nicely blow something often, I really get the impression that they believe it. And frankly, I can't figure out if they are just super-duper inefficient, delusional, or some combination of both.