I've actually had several close calls:
Once while turkey hunting I had a small doe come close enough that I could have poked her with my shotgun barrel.
Once while deer hunting I was crouched behind a blow down and someone spooked two does right at me, at the last second they split and jumped over the log a few feet on either side of me.
Once while walking out from an archery hunt, bucks were chasing does all over, and it was getting too dark to see. I wanted to climb down, but I didn't want to blow up my spot. So I waited until the activity died down, climbed down, gathered my gear and walked to an overgrown gas line right of way that headed towards my truck, all with no flashlight. As I'm walking up the gas line I start hearing pounding hoof beats. I stopped in my tracks trying to hear where they were coming from, and quickly realized that they were coming down the gas line right at me. I fumbled getting my flashlight out of my pocket and got it turned on just as a big doe lurched to a stop mere feet from me and swapped ends and took off. In those brief seconds I had visions of someone finding my sorry dead carcass with hoof prints going up my chest and down my back like some bad cartoon.