Okay, so I had this idea trotting in my head this whole time, but I ain't no economist, so basically I'm asking you to shoot it full of holes so I can see what's left. Science-style.
so let's get started. In a healthy economy, your money supply need to grow a bit faster that GDP growth, otherwise you get deflation which is a Bad Thing™. Not too fast of course, or you get inflation, but you want it to grow anyway.
Now, there is basically 2 ways to increase the money supply. The first one is basically to print money and have the government spend it in some ways. It was the traditional way to do things but I don't think I need to tell you what happen when you let politicians handle a machine that let them have cash now at the cost of inflation during their successor's term. So this way was phased out during the 1970's and 1980's. In Europe, the interdiction to print money ended up enshrined in the Maastricht treaty. Nowadays the closest thing we have is Quantitative Easing, that is the Central Banks buying sovereign bonds. The money still go to the government's coffer, but as loans, thus increasing the sovereign debt.
The second way is debt. It might surprise you, but banks actually don't have most of the money they lend. While they do need to have a percentage of their loans in real money, they can just lend you money they don't have. This way, every time you take a loan, you help creating some money and increasing the money supply. Now, the bank do need to have a percentage of "real" money, but they can just borrow it from the Central Bank. Needless to say, when banks borrow, that's another net cash creation.
Now I think you start seeing the problem. The only way we have to increase the money supply is debt. What we saw in the crisis aftermath in the U.S. was a huge rebalancing of debt as the federal governement effectively took over private debts. All the talk about "closing the deficit" is one big bullshit, as closing the deficit without contracting the money supply would require the private sector taking on huge amount of debts. Someone has to be in debt for the economy to work with our current system. And as the money supply increase, overall debts levels increase, no matter how austere we are. (Except if you crash the economy, then you don't need that much cash to buy your reduced output).
So what we need to do is clear. Print money. Print money for as long as the inflation is low enough. It's free money, but you can't depend on it, since we need to be able to cut the new money flow whenever inflation get a bit too high for our taste. My suggestion would be to pour that money in a state-owned investment bank, that would loan to business and invest in stuff like infrastructure. Another alternative would be a sovereign wealth fund, but Europe and the US are big enough that you don't need to invest in foreign companies.
Now, it is 2 am over here, so I might be a tad incoherent. I welcome your criticism.