Which is also a reason why many people go with the lowest bid. I'm sure if the Pegula's picking up the tab for overbudget costs, they already had a number they are comfortable with in total cost.
Some of the projects I work, I am given a budget to do a renovation and tell my boss we can't do it unless it's X amount of dollars for the budget. After a little back and forth he "finds the money" to get the renovation done. He already had a top dollar picked out but wanted to see what could be done first to limit hitting a higher mark.
The same could be said with the Pegula's. I'm sure they are being told "It will cost 1.4B" The first question I'm sure they would ask is "what is it going to cost if things are behind, go over budget, etc."