What is the minimum supply voltage for an LM335?

With 3.3K you are not getting 1mA. You are getting around 100uA.

At 25DegC the LM335 is at 3V. With a Vin of 3.3V you getting 0.3V across the resistor. 0.3V / 3.3K is apx 100uA. If you use a 300Ohm resistor you should be at about 1mA.