Yeah, fair enough. I work in a position where the deadlines for what we are building are mostly self imposed (we of course want to be competitive with other businesses that do what we do, so there is some sense of urgency, but it is not going to significantly impact the business if we late by a mont or two on something). While we do have deadlines, they are somewhat flexible as long as you can give a really good reason why you can't meet it.
I think the only thing you can do in this situation is to express frustration with whoever was involved in determining the 3 month deadline. You can only tell them that it is not enough time and that they should involve some technical people when making decisions like that. If they don't like what you have to say or the whole strategy of the company is actually based on doing things cheap and fast, then maybe it is time to move to a new company that has an environment which is more aligned with your values.
