Doesn't additional easing amount to little more than pushing on a string?
It does not, in my view. The reason is that, in my opinion, a determined central bank cannot fail to raise inflation expectations. The Fed has the ability to create as much money as it wants and can use that money to purchase every scrap of federal-government debt, every scrap of outstanding mortgage-backed securities backed by federal housing agencies, and as much foreign exchange as other governments will sell it. It strains credulity to think that the Fed could use its printing press to entirely fund the government and most of the mortgage market and to devalue the dollar with reckless abandon without having an impact on inflation expectations. In practice, it seems to take nothing like that to move expectations; a bit of tweaked language or a few hundred billion in QE purchases are enough to do the trick.
If you concede that the Fed can raise inflation expectations, then you concede everything. Higher expected future inflation raises inflation in the present, and higher inflation in the present simply represents more demand: prices rise because people are deploying more money, to buy assets and goods, to spend and invest. One hears the argument that higher inflation could hurt the economy by reducing real incomes, leading to less spending. But that's not how it works; if reduced real incomes lead to reduced spending, then you don't get the price increases in the first place. Prices don't go up unless there's more money chasing the same stock of goods.