Beating Nigel to the punch, why don't you use a 16F628? They do everything that the 84 does, plus they have built in voltage comparators. You simply load the appropriate bit pattern, as listed in the data sheet, into the comparator control register to set the configuration you want.
A friend and I did a very similar thing. Instead of testing a potentiometer and making a result, we made a capacitor tester. We have a known resistance value, and insert an unknown capacitor, and use a comparator to determine when it reaches a specific voltage level. When the comparator interrupt occurs, we use the value in TIMER1 to determine how long it took to charge, and hence the capacitance of the circuit. 8)
Or instead of using a comparator and a capacitor to test a resistor, why don't you use a chip that has a built in analog to digital converter that just works, as opposed to a software solution such as you are proposing?
By getting an analog to digital conversion, and simply outputting the results, your LEDs will count up or down sequentially in binary as you turn your potentiometer. If you would rather have something that rises like a volume indicator bar or something, perhaps just test to see what the most significant bit in the ADC result is, and then output all LEDs on up to that point, and leaving any higher ones off.