There are plenty of times when teams accomplish superhuman feats in the name of getting the impossible done. But in the world of on-going processes and management the concept of resource constraints are real. Some fall back on the excuse of “resource constraints are not an acceptable excuse.”
This concept is bad because either 1) you don’t trust that your team is being truthful about the situation and you aren’t willing to call them on it or 2) you believe them and don’t care. Either way implies that you are willing to simply push the problem downstream with no concept of the cultural damage you are causing.
You have now set a standard that unrealistic expectations exist and there is nothing we can do about it. Employees now have a decision: 1) do everything they can to achieve the desired goal even though they will likely fail and get yelled at or 2) ignore it and get something realistic complete and get yelled at anyway (or the ever popular door 3 of do nothing and get yelled at anyway).
Nothing good comes from this mentality – ever.