We know clients want quick work, but at the end of the day they won't accept anything less than perfect quality--no matter what they say at the hand off of the job when they just want to get it assigned.
I know everyone wants to win a project no matter what. And if you try to explain to the client what is really possible and what is not, you still risk losing the work to the many vendors who will say "yes" no matter what.
These are the aggressive vendors, both in India and China, who will take any project, whether they can really do it or not, on the hope that getting a job is the main thing and they will likely get some payment even if they can't come through 100%. This is the idea that obtaining some money now is more desirable than having an on-going relationship with a client.
However a more mature view is that you should not just be jumping through hoops for a client who wants something crazy--you need to be educating them on what is and what is not possible. This means telling them they are making a mistake by demanding the ridiculous and impossible.
(It should be noted that localization, for all the pretension our industry gives it, is simply "translation" in most companies and considered a little more than a back office administrative task. This mean the drones who are interfacing with you in handling the project have little power to do anything other than try to fulfill the insane demands their bosses made of them concerning the localization work. This means to make you pitch to change the way clients do things, you have to deal with those higher up in the chain of command who really can make the change.)
So when you get these rush requests, the only way to go is to ignore the client's wishes and quote the right time and price for what is really possible and they can take it or leave it.
Anything else risks a bad result that hurts your relationship.
In all my years in localization, I have been in too many staff meetings and spent too much time trying to figure out how to do stupid things for a client that just won't work and will mean disaster later on for the relationship.
The time should be spent on educating the client and making sure they know that the way they have decided on doing things will lead to disaster and all of them getting fired for botching the job.