Estimates are not deadlines. They never were deadlines. Real deadlines are contractual or legal - these are externally imposed, and should be communicated hones

Estimates are not deadlines. They never were deadlines. Real deadlines are contractual or legal - these are externally imposed, and should be communicated honestly as such, also with a clear awareness of the hard consequences of not meeting them. It your manager does not understanding that estimates are not deadlines, find one who does.