This is true in that you should never promise anything you can't deliver.
I do think you should over cut and then tell the remaining people that you have done this so that you can say you have done everything in your power to avoid doing it again. If you need to cut 50 people to have a good chance of surviving then cut 75 and tell everyone remaining why you have done this. One and done is critical.
You just might, and you'll lose all credibility with your employees.