I've been on both sides of this situation. As an engineer I'm always adamant - yep, no way this could be done any faster and please stop pressuring me to just get the number you want to hear. It'll be done when it's done, and it'll be robust and good. Now please go away and let me cook.
But when I've been the manager pushing for smaller estimates, it's been because the business realities were that delivering *something* in a given time frame is critical. And if it requires making a house of cards and cutting corners, well at least we'll have survived long enough to deal with that problem later. And when I've been in that situation I received the usual pushback from engineering - the same pushback I would give in their shoes - that this is a terrible idea, will doom us to fail in the future, and we need to put in the leg work now to avoid future pain.
I've gone back to being an engineer but that experience as a manager has helped me quite a bit when dealing with this sort of divide.