On another writers' list that I'm on, they've been harping on how you should always use "said," how it's the only acceptable way, blah, blah, blah... (can you tell I'm not in complete agreement? ) but like others here have mentioned, I think eliminating "groaned" and "whispered," etc. entirely could potentially lose a writer's voice, not to mention reading as boring copy.
I'd have to agree. Yeah, you can go too far with the synonyms. I've seen it overdone, and the story looked a bit silly. But IMHO, a little variety doesn't hurt. I think eliminating it all together in a section of dialogue doesn't hurt either, as long as there's no confusion as to who's speaking.