An issue arose in the Comments on my earlier post on suspending the gas tax regarding the tax incidence of this tax. The basic economics of taxes is straightforward--if the demand curve is relatively more inelastic then the supply curve the consumer ends up bearing the greater proportion of the cost of the tax. So if the tax is increased on a product with an inelastic demand curve, most of the cost of the tax will be passed onto consumers (cigarettes being the typical stylized example that is used). Similarly, if the tax on a product with an inelastic demand curve is reduced, then most of the tax cut will be passed on to consumers as well.
So to determine whether a gas tax moratorium will reduce prices depends on the relative inelasticities of supply and demand over the relevant time period.
This is an empirical question, and one on which there seems to be relatively little research. I've found two recent papers that suggest that consumers and suppliers each pay about half of the federal gas tax and that consumers pay a higher percentage of state sales tax (in one study, all of it). Chouinard and Perloff find that consumers and wholesalers each pay about half of the federal gas tax and that consumers pay all of the state gas tax. They argue that the reason for the difference is that the elasticity of supply is greater for state taxes because wholesalers can shift supplies among states more easily than at the national level. Consistent with the finding that consumers pay most of the state gas tax, a paper by Doyle and Samphantharak studied the impact of the suspension and then subsequent reinstatement of a 5% gas tax in Illinois and Indiana and concluded that retail gas prices are found to drop by 3% following the suspension, and increase by 4% following the reinstatements (the differences between the 3% fall and 4% increase were not statistically significant). They also concluded that some evidence suggests that the tax increases are associated with higher prices up to an hour's drive into neighboring states. Because they were looking at specific state-level gas taxes, they don't provide a separate estimate of the incidence of federal gas taxes.
So from what I have found in the sparse empirical literature, probably the best estimate is that about half of a federal gas tax moratorium would be passed on to consumers and about half would be borne by wholesalers.