It would be natural to start by supposing that a given English sentence means that P just in case when speakers of English utter that sentence, they always or at least normally (speaker-)mean that P.  But here come the problems.

    Obstacle 1:  Ziff's last two examples.  As I said, it seems to me that in his altered state, George did mean that he felt fine; and the madman derangedly meant that it was snowing in Tibet.  And I take the point to be that if Grice's theory of speaker-meaning is correct, then speaker-meaning comes very cheap: Given a suitably disordered mental state, any speaker may mean anything at all by any string of noises s/he happens to utter.  If Grice's analysis of speaker-meaning is correct, then, all the worse for Stage I, for there will then be no formal constraint on what speakers might mean by any sentence they utter, but only statistics about how often speakers do mean this or that.
    In real life, of course, speaker-meaning is not so easily had, for two reasons.  (a) Most people are not deranged in the manner of Ziff's patients.  Far more importantly, (b) English sentences have the meanings they do have, and one cannot just mean anything by them one likes.  Unless I am oddly mistaken about the meaning of the word itself, or some more elaborate stage-setting is in place, I cannot say "It's cold here" and mean by it "It's warm here" (Wittgenstein again).  I could be being sarcastic, of course.  But I could not very well mean "I have just rented the video of Agnes of God," or "Pigs have wings."  The antecedent meaning of a sentence partly controls what a speaker can mean by it.
    (b) further embarrasses Stage I, since if sentence meaning is to be analyzed entirely away into speaker-meaning, we should not have to look to sentence meaning as constraining possible speaker-meanings.  (Perhaps "should not" is too strong.  There is no flat-out circularity here; and it is certainly possible that one special construct out of speaker-meaning might constrain speaker-meaning in general.  But the Gricean will still have to explain why this happens so robustly.)

    Obstacle 2 (Mark Platts):  Most meaningful sentences of a language are never uttered at all.  Therefore no one has ever meant anything by them.  Therefore their meanings can hardly be determined by what speakers (normally, typically, etc.) mean by them.
    It is not much use, though it is tempting, to appeal to what speakers would have meant by the unuttered sentences had they uttered them.  For one thing, to echo Sophie's point about Grice's line on absent audiences, the vast majority of those sentences are ones that the speakers would never have uttered in the first place.  Even for a sentence that the speakers might have uttered even though they did not, the only handle we have on what the speakers would have meant in uttering it is what we already know that sentence to mean.

    Obstacle 3:  Novel sentences again.  Even when a sentence is actually uttered, it may be wildly novel, yet instantly understood by its audience.  But if it is novel, then no pre-established expectation or convention has been directed specifically upon it.  And notice that the first, novel use may be (a) also the last and (b) itself nonliteral.  I am pretty sure that the following sentence has never been uttered before, though it may be uttered again (it's a new variation on the one I produced in class): "The President of the United States Philosophy Corporation, who has finally been released from prison and is hurrying here to the aviary on winged feet, will share the riches of her spirit with us at 2:00 p.m. tomorrow."  In such a case, even though the sentence had been uttered, no one would ever actually have meant by it, what it literally means.
    My probably former colleague Simon Blackburn has pointed out that in the right circumstances, a given sentence may be uttered with practically any intention and certainly without the intention of displaying one's actual belief.  (Blackburn broaches the alternative idea that a sentence S means that P when it is either a conventional regularity or the consequence of a conventional regularity that one who utters S with assertive force "may be regarded as having displayed" that P, this regard-license being a social fact that obtains independently of any particular utterer's intentions.  This is an interesting idea, and calls for much unpacking of "may," "be regarded," and "display," but it is not a Gricean idea, for it self-consciously severs sentence-meaning from speakers' communicative intentions.)

    Obstacle 4:  Sentences are often, and not just abnormally, used with other than their own literal meanings.  Even neglecting sarcasm and other forms of indirect speech acts, figurative usage is very prevalent.  If Grice should want to say that a sentence's own meaning is what speakers "normally" do mean in uttering the sentence, he would have to say what "normally" means independently of the sentence's standard meaning, as well as motivating the claim.
    And things get even worse.  There are private codes in which a given sentence is never used with its literal meaning.  The Japanese signal for the 1941 air attack on Pearl Harbor was (the Japanese expression translated as) "East wind, rain," which so far as I know has never been used to mean anything but "It's time to go bomb Pearl Harbor."  And even apart from private codes, in everyday life there are many sentences that normally are uttered with other than their literal meanings, and perhaps are never uttered with those literal meanings.  ("I'd like some cake"; "All right, buddy, where's the fire?"; "Can you tell me the time?"; "George and Martha buried the hatchet"; "Business is business.")  And there is the whole question of metaphor.  Renee is probably right in saying that such sentences may at some time have been used with their literal meanings, but literal uses are at best rare.

    For Grice's ways of overcoming these obstructions, see the accompanying excerpt from my textbook.