DaveC426913 said:
Very different animal.
You are talking about a stepper motor.
You should go visit your local electronics surplus store. They will have what you need.
Most servo motors are not stepper motors, but instead use some kind of absolute rotary encoder (a potentiometer, for example) to provide feedback which is used to correct the output of an ordinary DC motor. Never seen a $3 servo motor, though, particularly not one capable of a full rotation.
Some other DC motors have optical or magnetic encoders built in. These are often quadrature encoders that are only useful for measuring speed and relative motion, you would need something else (a limit switch, photointerrupter, etc) to establish a reference point to measure absolute position. You would also need something to decode the quadrature signal and control the motor. A DC motor with gear reducing and encoder is also unlikely to be had for $3, and the decoder and control circuitry won't be free.
Stepper motors are also relative positioning, requiring a reference point to set a zero against, and also require special control circuitry. You can get some used/surplus steppers in that price range that might be suitable, but the control electronics will increase the overall cost.
Sources...look at bgmicro.com, jameco.com, allelectronics.com, e-Bay...really, just Google for some lists of places to get robotics parts. You also haven't mentioned what kind of quantity you want these motors in...you can probably get a box of motors for considerably less than $3/motor off e-Bay with luck and patience, or one or two $2-3 steppers from somewhere else, but reliable supply is another matter unless you're doing huge quantities.