Input rated current for easydriver 4.4
Looking at the two links you provided the voltage rating of the stepper motor is shown as 12V which you've well exceeded by applying 20V. That may caused it to exceed the 750mA rating of the driver or burnt out the motor, but when operated at 12V the rated current is shown as 330mA so that driver should be OK.

In general 'supplying' 3A shouldn't be a problem, because if operated within spec it won't draw that much current. But I guess you really mean you've attached to a 20V / 3A supply which would have been delivering less current in practice. So yes 3A would be too much, but I doubt it was really drawing that much current unless you also have some other problem, or the motor windings shorted because of the higher than rated voltage.