That's a good question. We're already playing that game a bit. Virginia, for example, introduced an extra registration tax on hybrid and electric vehicles, with the rationale that they're not paying their fair share of road maintenance from fuel taxes. It was subsequently repealed under the theory that the benefit from not polluting so much outweighs the tax losses.
My random guess is that we'll go to plain old mileage reporting. Fuel taxes for road maintenance may have made sense a long time ago, but fuel use and road wear are fairly weakly correlated now even among gasoline cars, since efficiency can vary so much now.
The problem with a mileage tax is that it would need to either be backed up with tracking (so an Illinois driver wouldn't be on the hook for miles driven in Michigan, as an example), or it would have to be a federal-level tax.
A possible alternative would be to tax the electricity at the charger, but that also opens up more cans of worms.
Another thing to consider is that, beyond normal weathering, most road damage comes from heavy (and often overweight) trucks.
I wouldn't be surprised if tracking happened. Pretty much every new car comes with GPS now, and it could be made to self-report. People would fight it (and I might agree with them) but I think it could happen.
I don't see taxing electricity at the charger as being viable, because it's too decentralized. You can tax gasoline because it's distributed by relatively few places. You can charge a car off a normal 240V outlet (or 120V if you don't mind it being slow) so it'll be way too easy to dodge.
Tracking mileage and assigning to the state of registration might not be too bad. It won't be fully accurate, but the inaccuracies will balance out to an extent. Gas already suffers from this at a smaller level, since you can buy gas in one state and then drive a substantial distance in another state.
The fact that trucks are the ones doing all the damage is a big wrench in the works. Maybe the proper solution would be paying some by taxing truck mileage and making up the rest out of general taxes.
Presumably, any state that does annual safety inspections already has miles-driven info (whether or not it's actually centrally reported today). You'd still need to deal with ownership transfers, collections, etc. but that would be one mechanism to charge per mile without GPS tracking--which (optimistically) seems like a real political hot potato.
I think that another alternative would be to increase the cost of vehicle registration as a percent of the vehicle cost. This way it is progressive and untied to fuel usage. Multi-car discounts could be given much like insurance (cars after the 1st do not add a full car's miles driven).
My random guess is that we'll go to plain old mileage reporting. Fuel taxes for road maintenance may have made sense a long time ago, but fuel use and road wear are fairly weakly correlated now even among gasoline cars, since efficiency can vary so much now.