The helicopter drop occurred?
Imagine every American who filed a tax return this year got a magical, fed-created refund of $100k...
Obviously the extra $20-30T in cash money would create real inflation, and in some places there would likely be shortages of some items (which would likely mean a serious jump in employment to meet demand and therefore recovery, Huzzah!). The dollar would also certainly weaken vs. other currencies, possibly by quite a bit.
I would guess that, in particular, the housing and construction markets would rebound strongly, since that is enough in many places to buy a house outright, and covers lots of renovation and other work that people would like to do.
I would also guess that gasoline prices would surge, possibly to over $6/gallon, and that heating oil would see a temporary spike. Precious metals would probably go through the roof on the combined front of some people buying jewelery, and other people trying to hedge against the now fairly certain inflation (pawn shops may sell out of gold/silver/platinum jewelery all together).
On the other hand, there isn't reason to think that all commodities, goods, and/or services would see increased demand--particularly not sustained--and some may see slack: people trading cooking in for restaurant dining or hamburger for steak. I mean, any given person can only eat so much. In addition, most people have a tv and a microwave, and unless an appliance is in bad shape or just particularly lacking, there isn't a huge reason to replace it. There may be lots of TV's sold right away, and that could create shortages, but once the rush is done, and everyone has the latest TV, sales would pretty much come back to normal.
Also, lots of people would use the money either as seed for something (starting a business, going to school) or to pay off existing debt (actually not a great idea in this case) and these things do not necessarily produce inflation. In fact if new businesses are started that are in competition with existing, then that could completely offset any increase in demand leading to pricing staying the same.
Assume this is a one-time jump and the fed removes this from circulation by selling off treasuries over a 10 year period.
Now pare that back to $10k each...
$2-3T extra monetary base in our current situation is far less likely to create much inflation. It may still weaken the dollar (strengthening exports, and domestic production). And that amount of extra money in people's pockets would create more demand, though not necessarily enough to cause shortages, this would likely lead to an increase in employment, which would, hopefully, create enough extra demand to get the recovery going at a brisk pace.
This isn't enough, however, to make a large impact on housing--if it spurred recovery, then that would come back into improved housing/construction, but not this on its own. It also isn't enough to make starting a new business as easy as it would be in the first case.
Because of the lower impact on housing, business starts, and inflation, using this for extra savings/debt reduction becomes a more attractive option, but that fights against the recovery, not for it.
Pare back further to $1k...
It seems this is an amount that would make a large difference to a very small subset of the population, but that would have a much, much smaller impact on the overall economy. For most people this would do much less; either they would save (or pay off debt) or they would simply shift a future expected purchase back in time.
I think the way to look at this is to see how much income and debt a person has and how much "free" money it would take to impact their behavior.
$10k/filer is probably the sweet spot between action and danger. That is a very large amount of money to most people, but the total increase in the monetary base is not completely ridiculous.