I know it seems a bit trivial, but what is the potential right at an infinite uniformly charged line? Irregardless of reference point, the Potential will have a ln|s|, where s is the perpendicular distance to the line. Obviously this would result in infinity. At the same time when I visualize a test charge on the line charge, the charge on either side of the test charge cancels and the result might be zero electric field on the line. This would result in a potential with respect to a reference point. But I suppose even this gives a potential of infinity, since there is the infinite potential difference between the reference point and essentially to the line.