No, the compass needle would not spin. At the magnetic pole, the magnetic field lines of the Earth are coming vertically out of the ground, which is perpendicular to the orientation of the compass. This means that the magnetic field is exerting torque on the compass needle, but perpendicular to the plane in which the needle can rotate (determined by the pivot point of the needle). As a consequence, the pivot point itself will exert opposing torque so that the needle won't bend out of its plane of rotation.
Now, if your compass were not held horizontally, then that would be a different story. Now, the magnetic field will rotate the compass needle to point downward (if on the magnetic north), or upward (magnetic south).
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