No, the pressure gauge should not ALWAYS read 3. I should read 3 when you are driving or putting any type of load on the engine, driving, reving, etc...

Once the engine is warmed up, the gauge should normally be around .3 to 2 when idle.

If you turn on the car, but DON'T start it, the gauge should read 0 since there is NO OIL PRESSURE. Upon startup, it should read some pressure. If you are reading 3 even when the engine is not running, then you have a problem. Either the gauge or sending unit is bad. Chances are it is the sending unit.