"How do you manage in these situations?". What I have seen / experienced:
the number 1 point I agree with Ptolemy: be honest:
If it is really a problem: go to that room, tell the problem, sit back to await the anger response and then ... work towards a new plan/solution. (the guy is not angry at you personally).
There are IT courses which deal only with this situation. You are placed with actors and they place the angry client who hears this news. You get a lot of tips around it. Sounds stupid but probably only after doing it you notice the value of it. I left with a sheet with 80 points to remember in those situations... (and practice).
This situation is typical probably even more so today where budgets are tight, sales are done on "lowest offer", the planning you gave is trimmed 5 times before it is accepted by the customer... (including that prototype since "he is hiring you because you are the expert and otherwise it is 10 others waiting") etc...
Another thing might be lateral thinking: if it can not be done in this way try to propose something completely different that provides the same value for the customer. If the technology does not work AT ALL / is broke / jumps out of the deal / etc... If the customer buys in to this it can deliver the same value at the end. But bringing it is also pretty hard. (for some and totally not for others). You need the really experienced guys for this. A likewise situation is that the Technology is NOT YET up to it... it takes some months... So you need to convince to customer to replan and accept the replanning and impact on his organization...
-- Another 'lesson learned' is to invoke the senior senior guys as soon as you notice that it goes in this direction. They often have dealt with troubled projects and are really helpful in these situations. Often they only travel from troubled project to troubled project.
-- Another lesson learned is to let your architectural stuff go through verification channels especially on the bigger projects. A signature can cover your ass. (save all your e-mails LOL)