If your offer is truly unacceptable in its present form you must communicate this fact in no uncertain terms to the decision-maker while keeping the outlook for resolution positive. Example:
"I am still very interested in working with you and your company; however (never use the word "but"), at this point I am not able to accept the offer for the following reason: (state your reasoning succinctly and what part or parts of the offer are lacking). If you were able to _____ (give your proposed solution), I would gladly accept the position immediately. Are you able to help bring this about?"
Take note of some of the key elements of this approach. First, you are putting at risk the job offer made to you since you are asking for a different offer. In terms of contract law, you have just made a counteroffer, which technically invalidates (and rejects) their initial offer. But if the initial offer is truly unacceptable to you, you need to be willing to accept the consequences. So if they are unwilling or unable to change the offer and do not extend the offer to you again, you are technically rejecting their offer.
Second, you need to communicate what is specifically lacking in the initial offer. Is it the position? The role and responsibilities? The money? Location? Insurance? Vacation time? You must name it specifically.
Third, you must propose a solution. Tell them exactly what can be done to make things "right." You need to make it understood that if this could be changed, you would be willing to accept the job. Immediately. On the spot. They will be much more willing to go to bat for you if they know that this is the last roadblock. Don't play the "you shot low so I'll shoot high" game. Be straight with them as to what it will take to make it happen.
Lastly, you need to appeal to their position and their vanity. "If you are able to…" is a positive challenge to the true power of the manager. If they really want you and your request is attainable, this will ice it. Very few managers like to admit they are powerless to get what they want. So if it can be done, they will make it happen.
It is already a given that the company wants you by the very fact that they made the initial offer. However, this does not guarantee that they will be able to respond to your request. Several factors may come into play. First, can they adjust the offer at all? Some companies have rigid "first offer is last offer" policies. And in most companies, salary administration tends to be more rigid at the entry level since comparable parity (what they are paying others with similar backgrounds and skills) is much easier to define. If they cannot adjust the offer under any circumstances, you are wasting your time and theirs and they will probably tell you so. If they are fixed on the monetaries, you might want to consider attempting to negotiate the near-monetaries or non-monetaries since these usually allow for some flexibility. But if the offer is still truly unacceptable, give them a polite "Thanks, but no thanks" and take your leave of them.
Second, what is the magnitude of your request? There may be restrictions regarding pay level within the position or benefits offered (only VPs get company cars, stock options, etc.) that cannot change. Be ready to consider alternatives if necessary (example: a sign-on bonus or mobile phone expense reimbursement in lieu of higher pay).
Third, what are their alternatives? If you are the only person in the world who can fill this position, they have very few alternatives and must work to make the impossible happen. But if they have two others waiting in the wings in case you balk, they may not have much desire to negotiate. On to #2, then #3, then #4 until they get an acceptance.
Again, this negotiation technique is the best approach when the offer is truly unacceptable, but it does run the risk of the entire deal falling through if you cannot come to terms. So use it with great caution.