Any decent project manager who wants to keep their job will acquiesce to people further up in the org chart who want deadlines, not estimates, and who consider the difference between the two to be as fuzzy as it needs to be.
A deadline is a requirement. It is not a PM’s job to reject requirements, though it is their job to help th customer understand and manage resolution of situations where the combination of requirements given are in conflict, such as when a deadline is insufficient to acheive the functional requirements.
And any decent engineering team will accept that a project has deadlines and raise progressively more serious risks with appropriate explanations up the chain as the confidence that completion will occur before the deadline declines below near-certainty.
Deadlines can be legitimate project requirements as much as functional requirements are. Identifying practical conflicts between requirements is part of what an engineering team does. Managing resolution of those once they are identified so that the customer gets the best result achievable is what a PM does.
