I agree with VE1BLL, for a 2V control signal I would go with an NPN transistor. The 2V will provide enough voltage to forward bias the BE junction and turn it on but the big question as he said is do you have enough current gain for your application. In theory, the CE current is the base current multiplied by the transistor's BETA. While many text books like to base design on BETA it is a poor choice practically speaking. As a rule of thumb, you should assume the minimum beta and then size the base resistor to give you a 10x overdrive for switching capability. To calculate the base resistance, take the applied voltage minus about .6 to .7V and divide by the needed current ((load current / minimum beta)*10). Then you need to also determine if your 1.5 to 2V source (which sounds like a gate off a PLD or other latch) can even provide this. If not, you may need to provide a secondary switching level with something like your IO supply voltage as the source instead of trying to directly drive the output from your logic.
The above assumes your using the transistor as a common emitter and providing the ground side of the relay coil. If you don't drive the transistor hard enough, it will turn on but be in the active rather than saturation region which means that your ground voltage will be high and the transistor will be dissipating a lot of power, but probably not for very long.