Why can't an object have "absolute" zero potential
Electric potential between two points is defined by:
$$V = -\int \mathbf{E} \cdot d\mathbf{l}$$
Where the integral is taken over a curve that connect the two points you are taking the potential across.

It is apparent that if you select any potential at point A, you can pick an electric field that will give you a lower potential at point B. Therefore, there cannot be a minimal potential i.e. the potential is not bounded below.