I do this on the lathe using a VFD-driven motor and the speed control lets me drop right down to zero. I start there and increase speed until the tap is cutting and at a speed that I don't feel is going to run away with me. In any event, the speed might be classified as dead slow.
I don't use this method at all for blind holes and frankly, at these speeds consideration of materials and cutting conditions are largely academic.
I would try to arrange the VFD setup to allow you to run down to zero speed (in can be handy in other situations too) but If you really need a bottom number, work out from the tap-pitch vs speed how long it will take for a tap to run all the way down and pick a minimum time that you think you can handle.
(All of the above assumes you are not using a tapping head, since you didn't say – if you are, then the manufacturer's recommendation should tell you what you need to know).
Edited By Bandersnatch on 25/04/2015 15:42:25