With inflation so low, why is it so hard to stimulate the economy? Usually the limiting factor in stimulating an economy is how much inflation can a currency handle before the money being spent has a negative effect overall. But now we seem to have the opposite problem of having a lot of leeway, but somehow we are not able to use it to stimulate growth.

It seems like in theory, we could print a bunch of money and do a helicopter drop at the expense of higher inflation, which would help since the US is almost in a deflationary state. Obviously central banks (mostly US but also the rest of the developed world) have better ideas as to what should be done to help the economy, and so I would like to understand what those ideas might be and why they cannot take advantage of the low inflation.
It's not theoretically hard to stimulate the economy. It's just the means to do so are terribly unfashionable. And that means it's politically hard.

We've had two similar depressions in the last couple of centuries: the Long Depression in the second half of the nineteenth century, and the Great Depression in the first half of the twentieth. Each saw significant monetary contraction as a policy response. Which was astonishingly daft.

But after the Great Depression, we also learnt that monetary expansion was insufficient when there's a large debt hangover and demand is suppressed: hence we got the famous analogy of monetary expansion being like pushing on a piece of string.

For many centuries, a once-in-a-human-lifetime jubilee - a cancellation of all personal debts - was seen a way to cure these huge debt hangovers. And they do, broadly speaking, provide a means of cutting the closed circle of monetary expansion which takes place through savings and loans. These jubilees used to happen once every fifty years - and that was, roughly speaking, a human lifetime. A jubilee removes all of the demand-suppression effect that personal debt has: it removes wealth from those with the lowest propensity to spend (thus has a small negative effect on demand), and increases the wealth of those with the highest propensity to spend (which has a much larger positive effect on demand). The net result is a return to increasing demand. In some ways, the bailing out of the banks in 2008 was the very opposite of a jubilee: commercial borrowers (bank bond-holders) were bailed out, and private borrowers were left hanging. Expensive and ineffective. A jubilee cancelled all private debt, but did not touch commercial debt.

The other very unfashionable intervention is fiscal expansion. Keynesian expansions were a successful response to a demand-led depresssion, when the multiplier was higher (as it is now: even Lagarde of the IMF admitted this); but they also got used in subsequent decades in other circumstances too, when the multiplier was lower, and showed less success. And that's when they dropped out of favour, and remain so in many countries now, despite them being part of the right thing to do in the current particular circumstances.