The inflation threat that we face doesn't come from deficits or high employment it comes from the cost and price of energy. But managing this is not within the competence of the Federal Reserve.
I have been trying to call attention to this issue for years (it's in my 2008 book, The Predator State, and in articles written recently with Jing Chen, most recently in the Cambridge Journal of Economics, which contains the following paragraph:
Our central argument is that stimulus fell short and would have fallen short even if the amounts had been greater because increased demand under existing high-fixed cost structures drove, or would have driven, the price of resources too high, too quickly. The constraint on growth was not inflation generated by easy money, but the combination of the rising real marginal cost especially of energy, combined with monopoly control of and speculative instability in energy prices, which together act as a choke-chain on the return to full employment.
But the endless debate over deficits, debt and quantitative easing tends to obscure this issue and in public discourse one cannot easily answer questions that are not being asked.
