Since energy is a larger percentage of low-income household budgets, energy taxes are regressive by nature. That regressivity can be offset in any number of ways. In fact, it could be offset with a relatively small portion of the revenue -- the Center on Budget and Policy Priorities estimates it would take 14 percent to hold low-income consumers harmless. The feds could do it by reducing payroll taxes, funding efficiency programs, issuing per-capita rebates, or some mixture thereof.
The regressivity can be offset, but will it?
Not if the GOP can help it. For them, alas, cheap gas is about as fundamental as the Second Amendment.