I’ve found myself in these spots several times in my life. Either I had to deliver on an estimate or I had to acknowledge an estimation and deal with the outcomes.
If you are involved in anything digital / software this is a recommended piece to read:
Anyone who built software for a while knows that estimating how long something is going to take is hard. It’s hard to come up with an unbiased estimate of how long something will take, when fundamentally the work in itself is about solving something. One pet theory I’ve had for a really long time, is that some of this is really just a statistical artifact.
Why software projects take longer than you think