Maybe I'm just conductive, but I can feel 120v just fine every time I latch onto it, which has been plenty of times over the years.
For the curious, it feels to me like a strong 60Hz vibration localized where the current is entering your body and spreading out to the exit point, though I always seem to feel it in my head too. It kind of hurts and is extremely attention-getting. If you are slow getting off of the contact point, it throbs and buzzes and is pretty unpleasant. "Shocking" is a good word for it, actually.
If you carelessly give it a good path to ground that goes through your necessary bits (one hand on the breaker box, one hand on the hot wire, for example), even low voltages can kill you. As current is a function of voltage and resistance, lowering your resistance makes it much more dangerous, and raising it makes it much less dangerous. The reason I usually experience shocks as mildly painful is that I do not set myself up to be a good path to ground when playing with hot wires (thick rubber soles, only one hand near the voltage, no other bits touching grounds or neutrals).
Someone with half a brain would set themselves up to not be working on hot wires in the first place, but I learned this stuff on 540v 3-phase systems with 50KV klystrons, so I tend to not regard 120v as "real" voltage, though it assuredly is.