If you are organized you can call their bluff. But if more than a couple of people defect and keep insisting they can make the unreasonable deadlines, then those people get attention because they are saying what management wants to hear.

One of my goals in life is to get better at identifying (read, admitting/accepting) when the team has defectors and finding someplace else to apply my skills. But the few times it has actually worked are a mighty incentive to try again, even when I should know better.