At this point, hopefully the warring parties have settled on an option. If they haven't you may have to make a decision yourself -- but don't do it now. Say "I'm sorry we haven't been able to come to an agreement, we'll meet later and I will make a decision at that time, based on our discussion at that time." If you decide now, based on what you've heard now, people will always be selling to your decision at this stage in the process, not trying to resolve conflict.

But, hopefully, an option has been chosen. At this point, it's important that everyone be able to sell the solution to their constituency. Help them out with this. Provide ammunition as necessary. And, if someone tightens up and tries to back out or gain leverage at this point, just return to the earlier stages of the discussion. Move backwards to deal with a single point, and you can move forwards to conclusion.