I used to live in Alaska, where questions of energy policy were quite important.
Economic analysis of the incidence of taxes is often considered in the context of the time frame. The short term incidence of a change in a tax is going to be different from the longer term incidence.
In most simple partial equilibrium models, the incidence of changes in taxes depend upon the relative elasticities of supply and demand. The least elastic factor is impacted the most.
Although estimates vary, the short term elasticity of demand for gasoline is probably around -.2, meaning a 10 percent increase in the price would lead to a 2 percent decrease in consumption. Demand for gasoline is relatively "inelastic," in the short run.
What is the short term price elasticity of supply of gasoline? In the short run, prices are driven by global crude oil prices, and the USA is pretty much a price taker in the global market. For US gasoline consumers, the elasticity of supply is pretty high, at least within the range relevant for small short term changes in US consumption of gasoline. (For larger changes in demand, and for longer time periods, things will be different).
In the short run, most of a reduction in excise and sales taxes on gasoline will led to reductions in the prices consumers pay at the pump. (Think of the short term impact of an increase in sales taxes.).
If the gasoline tax revenues are replaced by an excess profits tax on oil companies, it will be a progressive change, shifting the incidence of the tax from consumers to shareholders of oil companies, including foreign share owners.
Some economists will be troubled by the Clinton proposal because it would increase consumption of gasoline at a time when policy interventions normally would seek to decrease consumption. But when addressing short term shocks to the economy, something like this can make sense. Consumers of gasoline include people who have to commute to work, and who can't easier replace poor mileage vehicles. As a short term measure, it is a respectable and progressive effort to protect consumers who have few options.
In the longer run, taxes on gasoline should be higher, not lower, to discourage consumption. But in the face of a rapid increase in the global price of crude oil, the short term proposal by Senator Clinton would be a reasonable and effective intervention.