This article describes the plan:
"The Obama administration has floated a transportation authorization bill that would require the study and implementation of a plan to tax automobile drivers based on how many miles they drive. "
As others have pointed out, there already IS a such a tax. The US federal excise tax on gasoline is currently 18.4 cents per gallon (more for diesel). Adding in other local/state taxes and the national average of taxes per gallon is 48.1 cents per gallon (more for diesel).
Using 22.6 miles per gallon as a rough estimate for the average fuel efficiency of a passenger car in the US, we see that for every 100 miles driven:
- about $2.12 is paid to local/state/federal governments.
- about $0.81 of that figure goes to the federal excise tax.
Apparently Obama feels the government deserves more.