Then I make more promises and estimates, playing the emotional card of "sunk cost" to convince upper management to continue funding the team rather than torpedo the project. Then we ship, and I quickly get everyone on my team promoted "because we shipped" before it becomes clear to upper management that we shipped something essentially worthless to the company. Because we're in a huge profitable company, everyone can jump ship to the next shiny thing, and whoever is left holding the potato on its way to deprecation just gets re-org'd when it gets canned.
I know it's a bullshit game. But I play it well, and all the software developers on my team get paid and promoted because I am so good at it.