Why does an infinitely decreasing resistance infinitely increase current?
Your basic misconception is that voltage is "supplying the electrons".  The electrons (or whatever the charge carriers are in whatever material you are using) are always there.  Voltage is the push to get them moving at the macro level.  It is this motion that we call current.

Current therefore is a function of two things, how hard you push on the charge carriers and how much the material resists the movement of these carriers.  Double the voltage, and you get double the current at the same resistance.  Halve the resistance, and you get double the current at the same applied voltage.

In theory, the current would go infinite as the resistance becomes zero.  In practise, the voltage source won't be able to support more than some current before it can no longer provide the voltage.