I don't think anyone other than "Will sign for slot money" players ask for only slot money... everyone else asks for at least a little over slot. "May sign..." is usually slightly more, "Undecided..." is quite a bit more and "Probably won't sign..." is at least $6,000,000 and usually $8,000,000 or more.
I have had at least one "Probably won't sign..." take my initial offer (when I certainly didn't want him to), but "May sign..." & "Undecided..." seem to accept the initial offer pretty often, and almost always not reject you outright (as in, they come back asking for more money... which you DO NOT need to offer to get a compensation pick)