Look, let's get one thing straight: V=IR. If you take two "ideal" 3.5V batteries and put them in parallel, what you read across the parallel pair is still 3.5V. If you put that voltage across a 1000 Ohm resistor, you'll get 3.5mA - the same as you'd get with one cell alone! That would be true no matter how many 3.5 volt batteries you put across the parallel bundle. If you try to "burst" the current by shorting + and - terminals, the current you get depends on a whole bunch of stuff: internal resistance, battery chemistry, the rearrangement of charges in the battery electrolyte, temperature change, etc. And, as was pointed out, it's never a good idea to just short the terminals out, particularly in a lithium battery.
What does change when you put the cells in parallel is the amount of energy stored in the whole system. This is frequently expressed in Watt.Hours (or, if you know the open circuit voltage of the cell, Amp.Hours.) So in an ideal case, doubling the cell volume (putting two cells in parallel) could double the Amp.Hours, NOT Amps!
That is, there'd be twice the energy stored in total system. You'd get the same current for a longer time. But even this may not be quite true. Nothing is ideal! If the open circuit voltages and internal resistances of the cells you put in parallel were different, you may stress out one battery over another (as pointed out elsewhere) and that battery may not supply the same amount of energy as the one next to it. Quite simply, the "stronger" battery might pump current into the adjacent battery and rob the load of useful energy in the long run. I know a lot of other people responding were driving at this. I thought I'd just put it in a more physics/chemistry setting.