You may encounter sometimes parties who are tough on bargaining; persons that take hardened, inflexible stand; persons who end their statements as they begin, 'Thus far - no further' types.
Remember the mediator has a job cut out. The first attitude is not to be judgmental to condescendingly suggest that there is nothing that could be done if the posturing is tough and mediation could succeed only on a policy of give and take. The technique is making the parties realise it without expressly saying.
The tough persons may begin to show impatience from the very beginning and make an opening statement that s/he does not have much time to waste. S/he cannot keep bargaining back and forth. It is best for you as a mediator to respond that you recognise her/his value for time and suggest that a time line ought not to be a problem and you are interested in eliciting the best proposals from both the parties within the shortest time.
The person may be worried about several constraints that operate. Maybe, s/he has to take the consent of someone else; maybe his/her boss has set a resource constraint; maybe his/her parents will not agree to the suggestion. Use the caucus to elicit the constraints if any and see how other's views could be accommodated in the talks and your honest view of such a course. It will assure the party of your earnestness in engagement.