EDIT - Just realised, this may belong in the multiplexing forum...
I hope you're not trying to run 1-Amp through an analog multiplexer channel.
so 5v peak to peak and only a few mA are the requirements.
It is only an issue if there is sufficient current flowing to drop a voltage across it that could interfere with your measurements.
The monitoring cell in a wideband sensor is maintained at 450mV by the pump cell, so adding an ohm or so there would offset the result into the controller - this however would be a known, and I could account for this in software. Unfortunately that's not the case with the calibration resistor.
adding an ohm or so to this resistor would throw the sensor way out of cal.