I disagree with Greg. Sort of. The fact that you lost a finger in the first few milliseconds of the operation will be of minor concern compared the being skewered by the bar when it flies off the bit and penetrates your chest.
I have a little Unimat machine, a combination micro-lathe and mill, that I bought years ago that is ideal for small work like this. Unfortunately, they ceased production back in the '80s, but units might be found on the used market.