would charging a tesla model S dramatically increase my monthly electric bill?
I am no expert, but from what I have heard from owners near me is that they do not spend even 1/10 of the amount normally spent on gasoline on keeping the car fully charged. Of course this depends on how much you normally spend on fuel in the first place, but the point is that if you drive less than 10 miles a day, your electric bill should go up such a small amount that you will not even notice. Depending on where you live, you can get a nearly depleted battery fully charged for about $5. Compare that to a tank of gasoline, which at about $3.30 per gallon at the least, on a small car would cost about $50 for the same amount of range.
It depends on how much you drive every day, what your electricity costs and whether or not your utility offers TOU (time of use) electricity rates. These are programs that allow for lower rates during the night when you'll be doing most of your charging.