Once the velocity of money picks up, the trick the Fed will need to perform is to take all that cash they printed back out of the economy.
The problem is that the Fed put cash into the economy by paying top dollar for assets. Because of ZIRP, they paid the maximum possible price for those assets, which means they will not be able to get the same price when they sell them. No one is going to pay more for those assets than the Fed paid for them, and that means they will not be able to pull out all that cash they printed. And that means inflation.
Imagine a bond with a $100 face value. If you were an investor, you might bid $50 for that bond, and then you would collect the full $100 when that bond matured.
But imagine if another player came into the market and offered $99.999 for that bond? Clearly, you won't outbid them. So they get the bond.
That is what the Fed has done. They put $99.999 into circulation with that bond. They printed that money from nothing. If you had bought the bond for $50, you would have paid with existing money, and therefore no extra money would have been put into circulation.
To get new money into circulation, and a lot of it, the Fed had to outbid everyone else.
But now they have a $100 bond they paid $99.999 for. When it comes time to sell that bond so they can soak up cash and burn it, who is going to buy it for $99.999 or greater?
Nobody. That's who.
They will have to sell it for less than $99.999 to get people to buy it.
Let's say they are able to sell it for $95.00. The end result is an extra $4.999 in circulation they can't get back out.
Inflation. But you won't see it until the economy begins heating up. As long as things are sluggish, all that extra cash is buried in back yards.