Massive increase in the cost of public transport as buses pass their tax costs onto users.
Massive increase in the cost of freight shipping, which would be passed on to consumers, i.e. everybody, since virtually every part of the economy depends indirectly on freight transport.
It would amount to everybody paying, and thus being more or less equivalent to public funding of roads.
Public Transport -- If tax payers are currently paying for the external costs of public transportation (via taxes to repair roads) then it won't cost anymore public money if taxpayers continue to cover that cost. For private busses this is a case of tax payers unfairly subsiding their external costs.
You could obviously tweak legislation to treat such vehicles differently if you wanted. I was just getting the core idea across, not suggesting my comment should be copy-pasted verbatim into the next bill Congress is passing.