You don't necessarily need the LM317 to do this. It sounds like what you want is a constant current source, which will force the same amount of current through a variable load (up to the limitation of the input voltage).
A basic way to do this is with a current mirror, which is shown below.
Your input is on the left (V1 at 2.755V as you have specified). The reference of 2mA is set by a resistor Rref (it happens to be 1k, but it depends on your transistor and your input voltage, you can adjust it if you need more or less current). The current which goes through the reference resistor is mirrored onto the (variable) resistive load (which is designated Rload).
My version of SPICE does not really simulate potentiometers, but I have used a macro instead to simulate the resistance from 100 Ohm to 1 KOhm in 10 steps (100, 200, 300...1000 Ohms). The current through the load potentiometer is shown below. Different resistances are in different colors; it is small, but the scale on the left goes from 2.095 mA at 100 Ohm to 2.060 mA at 1 KOhm:
Notice that there is a small variation (on the order of several percent), but the current mostly stays around 2mA - even though the resistance changes by an order of magnitude.
You should look up the Wikipedia article on current mirrors as well. Clearly there is a limited range for which the current mirror will continue to give you 2mA; for example, if you make the load 10 KOhm, it will not work since the voltage across it will need to be 20 V alone (not counting any drop in the transistor).