Considering that every independent estimate puts the money saved at slower to $90M than $200B, yes, running around thinking you have 5 orders of magnitude more effect than you do is a bad thing.
Add to that that most of the things cut, for example weather forecasting, has returns to the economy of several times what is spent on it, and the damage to the economy is much larger than any savings.
Add to that that most of the things cut, for example weather forecasting, has returns to the economy of several times what is spent on it, and the damage to the economy is much larger than any savings.