I am not sure I understand your wiring. Are you wiring the sensor up like that:
Vcc AIn1 AIn2 Vcc
| 1k | R1 R2 | 1k |
, where R1+R2 = Rpot (10k?) ?
What is the advantage of that with respect to a regular pot wiring (Vcc, out, Gnd)? That you can detect when the pot is actually pressed by comparing Ain1 vs Ain2?
And when you connect multiple softpots, how do you wire them?
With these resistor values, I do not see any problems with too much current being drawn. What are you using as Vcc?