Neil Irwin observes that whether or not you want to, you actually can't inflate away the long-term deficit because of the nature of the commitments. You see this most clearly with Social Security, in which the monthly benefits are specifically pegged to the inflation rate, so trying to inflate away the obligation would be self-undermining. But it's also true for Medicare and Medicaid, in which the government commits to paying certain kinds of bills. General inflation doesn't make hospitals cheaper or doctors more plentiful.
That said, the malign influence of Carmen Reinhart and Vincent Rogoff on national discourse has created a morbid obsession with the debt-to-GDP ratio. The Fed can help with this. What Reinhart and Rogoff did was look at a bunch of countries, their debt:GDP ratios, and their growth track record. What they found is that slow growth is associated with a high debt:GDP ratio. This is obviously because slow growth of the denominator leads to a high ratio, but for reasons that are mysterious to me they chose to make the clearly incorrect causal inference and say that a high ratio leads to a slow-growing denominator. Because this suited various people's political agendas, the obviously wrong causal inference has become part of the Belway conventional wisdom and people are now very worried about the debt:GDP ratio.
The good news is that a lot of that debt is owned by the Fed. And the Fed could just tear up the bonds. Or, equivalently, promise to never sell them. That would make the debt:GDP ratio magically lower.
You might worry that this would be inflationary. I think that it probably wouldn't be unless the Fed explicitly stated that they wanted it to be inflationary. And the Fed could always use higher interest on excess reserve payments to fight any inflationary impact. But even better, according to Reinhart-Rogoff conventional wisdom, the reduction in debt:GDP ratio would actually cause more rapid real economic growth. A higher price level is a small price to pay for substantially faster growth in real incomes and living standards. Now, you might look at this argument and say it's nonsensical to believe that the Fed arbitrarily adjusting the debt stock downward would increase real growth. And, indeed, it is pretty nonsensical. As I say, the Reinart-Rogoff causal inference is not only mistaken but, in fact, obviously mistaken. Yet lots of people claim to believe in it and, in fact, claim to believe the debt:GDP ratio is a huge problem. Under the circumstances it's a bit odd that they're not pushing for the obvious solution.