electromagnetics is not really my forte, but if you pick up an engineering physics text like Serway's Physics for Scientists and Engineers, you'll see that if you integrate the electric field, E, on a path through your infinite resistance, that the result is voltage. this electric field, E, is in units of N/C or V/m.
now, if we assume that the resistor is uniform, and therefore the field throughout it is distributed uniformly, then E is a constant value on your path integral. and when you integrate a constant, the result is a line. so voltage through the resistance is a linear function with a value of 0V at the reference node, and 100V at the other end. a 1-meter resistance then has an internal potential of 1V at 1cm, and 63V at 63cm.
note that it doesn't matter if an electron can "fall" through this field and create a current or not, the field, and therefore the voltage, is still there. same deal with a big boulder sitting on the ground. no masses are falling through the center of it, even though there's a g field permeating the rock. but at any point h within the rock, there is a potential energy of mgh that would be associated with a mass falling from that height to ground level. this isnt' the exact analogue to voltage, but the form is familiar.
Makes sense, but this is not really regarded as voltage drop (kinetic energy) its actually potential that premeates the infinite resistance......is there a term for this?