Do lower fuel prices create jobs in the US?
So, the answer really is dependent on the overall state of the economy as well as the fuel price itself.
Look, free trade, free market, makes job argument is all fine and dandy other than the fact that it is never applied across the board. It's only made as a justification for something of interest to larger corporations and industries. Keystone pipeline ? Creates jobs, no doubt. Increased oil and gas production ? Creates jobs, no doubt. Increased export of oil and gas ? Doesn't create a single additional job if overall production and recovery doesn't increase.
If there's no requirement to supply the domestic market first there's no reason to believe that a shortage here while sales boom overseas is of any great concern to the producers. After all, the domestic market can just deal with expensive industry and whether any industry other than their own is creating jobs is not their concern, right?
It's the difference between a wolf pack and a dozen independent feral dogs. Wolves care about the overall good of the pack, feral dogs don't. Most arguments about letting the free market work have, over the past few decades, have become arguments for the right to behave like a feral dog rather than a member of the pack.