David Leonhardt had a thoughtful piece about the Fed's decision to accept higher rates of unemployment rather than engage in more aggressive quantitative easing to boost the economy. At one point he asserts that:
"There is a direct analogy between the budget deficit and the Fed’s
asset holdings. Neither is sustainable. Congress needs to
demonstrate that it has a plan for reducing the deficit over the long
haul so that investors will be confident enough to continue lending
the United States money at low rates.
The Fed, meanwhile, has to show it has a strategy for selling the
trillions of dollars of assets it bought during the crisis — without
damaging the value of private investors’ holdings and without, at
some point, igniting inflation."
It is not clear that why continued holding of assets is unsustainable. Japan's central bank has been holding vast amounts of the government's debt for more than a decade and yet it is still in the situation of fighting deflation. In the context of sustained economic weakness there is no obvious way that holding government assets will lead to inflation.
Furthermore, even if the economy was to rebound, the Fed has other mechanisms for preventing inflation, such as raising reserve requirements, which can allow it to continue to hold assets without causing inflation. This is an important point because it means that the debt accrued in the midst of a severe downturn need not impose a substantial interest burden on the government in future years. The interest on government bonds held by the Fed is rebated to the Treasury, creating no net cost to the government. There is no obvious reason why the Fed can't hold a substantial amount of the debt accrued during the downturn indefinitely while using other mechanisms to stave off inflation.