Some remarks:
It would work if you give money to poor people - who instantly buy things with it.
True, and that works a lot better than stuffing the banks until they are flush with money nobody wants to borrow for investments because there are not enough customers with money to buy products. A problem in the USA, however, is that even if you create customer buying power somehow, most of the products that will be bought are made outside of the USA, so it will create jobs in eg. China, but not in the USA.
Another point is that the USA government borrows from the FED and pays interest by choice. The FED creates the money out of nothing, the USA government could do the same and have the money interest-free and without incurring debt. The result for the total money supply would be the same. Inflation will only be a problem if production can't keep up with the increased demand from the increased buying power if the money actually gets into circulation.
Helicopter money (as in: giving money to consumers, in whatever way) is completely different from quantative easing, the latter mainly increasing the amount of money in banks where it sits doing nothing. It is the demand side that needs work, and getting production back to the USA. After all, if you can kickstart an economy by killing Germans, other ways can also be found.