Target dates you are asked to hit can easily become anchors for your estimates. This could bias the way you think about the effort that will truly take to complete something.
If possible, try to come up with your estimates before a date is planted in your mind. If you know beforehand, try not to work backward from that date because you'll increase the chances of biasing your estimates. Put the date aside, and estimate your work trying not to think about it.
Anchoring is a real threat to accurate estimation. The further away you get from it, the better the outcome will be.