This is a reasonable approach, and it should be studied.
As gasoline consumption decreases due to more efficient vehicles, and different forms of propulsion, the amount of tax revenue from gasoline taxes will decline. A sensible approach would be to tax the common denominator--miles driven--rather than the fuel type. Electric cars should not free-load on highway taxes.
The devil is in the details, of course. Americans will not put up with an intrusive enforcement system, such as mandatory monthly mileage checks. In states which have annual emissions tests, they are roundly hated, and removed whenever the voters have a chance. A less frequent annual or quarterly mileage check would result in higher tax bills, as opposed to the gradual leeching we get from gasoline taxes or toll roads. I would support an electronic system which allows cars to report mileage wirelessly to road-side sensor, or RFID based toll gathering sensors, however privacy hawks will howl that Big Brother is going to know where we drive.
Another detail is the amount of tax--people who pay a mileage tax should not have to also pay an equivalent gasoline tax. It should be one or the other.
Taxing miles has another side effect, which is to put direct pressure on the number of miles driven. As fuel economy increases, each mile driven will become less expensive. By keeping miles expensive, the government is encouraging less driving, which will lead to less wear on the roads and less damage to the environment.