Not now exactly. In the UK, for example, the MPC has scope for some further reduction in interest rates. (I think they should use that scope now, but that is for another day.) But, as Mark Blyth, Eric Lonergan and I argue in the Guardian, if something serious goes wrong in the next year or two, or if another financial crisis happens in the next decade or two, monetary policy is under equipped.
Does this mean that I no longer think it is a good idea to have a fiscal stimulus in a recession when nominal interest rates are at their floor? Of course not, because helicopter money is essentially just like a tax cut. What is true is that helicopter money is not my ideal form of fiscal stimulus, partly because there is some uncertainty about how much of it will be spent. I would much prefer additional public investment, for which there is a strong microeconomic as well as macroeconomic case.  Michael Spence  is one of a huge list of eminent economists, which includes Ken Rogoff, who think additional public investment across the OECD would be beneficial.
We should continue to urge governments to recognise this, but we also have to accept the awkward fact that they are not listening. In political terms, the need to reduce deficits trumps pretty well anything else. (Perhaps things are turning in the US, but until the Republicans start losing power I’m not counting chickens.) One of the many depressing things about the Conservative election victory in the UK is that it looks like deficit obsession is an economic strategy that can win, as long as the austerity is front loaded, which is why Osborne fully intends to do it all over again.
Because helicopter money is mainly a form of fiscal stimulus, and because the case for fiscal stimulus in a liquidity trap is largely agreed by most academic macroeconomists, the debate over helicopter money is essentially an issue in political economy. Persistent demand deficiency is clearly preventable, and represents a huge economic cost to society. Politicians will not do what economists call a bond financed fiscal stimulus because spreading scare stories about public debt is a vote winner. That leaves us with a money financed fiscal stimulus, of which helicopter money is one form. With independent central banks, that means giving these banks the power to undertake helicopter money.
I think the biggest obstacle to helicopter money is probably central banks themselves. This is for two reasons. First, they seem far too optimistic about the efficacy of creating money to buy financial assets (QE), even though they almost certainly need to create far more money by this route than they would through helicopter money, with a far less certain impact. Second, there is this residual worry that creating money now will mean they will lose the ability to control inflation in the future, as if a modern government in an advanced democracy would ever refuse to provide them with the assets they need.
The consensus among macroeconomists is that independent central banks are a good idea. The belief is that the business of macroeconomic stabilisation is best achieved if the task is delegated. But making central banks independent is not the same as completely delegating the task of macroeconomic stabilisation, because of the problem of the lower bound for nominal interest rates. Indeed independent central banks made the obvious way of getting around the lower bound problem, which is a money financed fiscal expansion, more difficult to achieve. Helicopter money is a way of making the delegation of stabilisation policy complete.