In Pennsylvania, where whitetail abound, it's very easy to kick up a deer while walking, as some will wait to the last minute, thinking they are well hidden...then bolt in front of you.
It's very rare for me to use a shotgun to hunt deer...tho there have been special PA Game Commission hunts in semi-populated areas that you are only allowed a shotgun with buckshot, to prevent misses from leaving the woods and endangering the population as well as property.
I usually stick with my Winchester 1894 in .30WCF. It has never let me down, with most snap shots well within 100 yards.