I'm having trouble understanding how this can be possible. Obviously, I'm missing something but I'm not sure what it is.
The amount of voltage at a point depends on the electrical potential energy at that point, which depends on the density of charge (electrons). So how can the voltage drop if the density of charge can't change, since that would cause a change in current.
I've tried thinking about it two ways and run into problems each time…
The charge density does increases but the speed decreases causing the same current. But if this were the case, and the density did increase in the resistor, then the resistor would have a higher potential than the wire and charge would stop flowing.
The charge density decreases across the resistor and the resistor acts like a funnel, creating a higher charge density at one end than the other. But the difference in charge density is counteracted by an increase in speed, allowing the current to remain constant. However we know resistance slows down charge, it doesn't speed it up.