It is an odd sensation. I am puzzled about some decisions that are quite unanimously recognized in literature as bad, or, if you prefer the buzzword, as anti-patterns. Forests have been sacrificed for books on the matter. Given the current (poor) state of the planet I would urge management to read them, not just having them to preserving their libraries from dust.
You have this project late, the customer is coming screaming at you because you didn’t made it for the milestone, the product is still alpha quality when it ought be on the shelves. Sounds familiar? If not either you don’t work in any technologically advanced sector or you have been unbelievably lucky (or good… or both). So it is clear that the project needs extra time to achieve the goal set. I understand that there are contracts and politics involved, but for the sake of the project there is just to plan and move the milestone ahead WITHOUT adding new features. Leave them for another project. The customer could be disappointed from this refusal but she will be a lot more disappointed when you’ll told her that you didn’t made it another time.
Disclaimer: I have to be honest, this is not my project, I don’t know exactly what has been agreed on, the only thing I know is what a coworker told me in about a single line: milestone postponed, new features added. So basically I don’t know what I’m speaking of.