I never say “No”.
I just say, “Yes. And this is what it will cost you to do it right:”
- Projects X, Y, Z will all be pushed back 2 weeks.
- Prerequisite Project will have to come first.
- weeks overtime for people = $z.
- Joe and Mary will have to be pulled away for 3 weeks.
- Interim solution will only take 1 week, but won't work.
- We will need your top supervisor full-time next week.
or, best of all:
- We don't know. We need a project to find out.
Note that “doing it wrong” or “doing it quick & dirty” are not options.
People understand “this is what it will take” a lot better than “no”. They also understand the trade-offs and sacrifices needed. Then they will work with you to make the best decision for everybody.