Economic growth has been very slow and risks returning to retrograde. The appropriate solution depends on the diagnosis of the problem.
If one views the recession as one of demand, a financial one, the problem is nominal and the solution is to provide more money. This could be the monetary authority purchasing other assets increasing their prices and introducing more money to the system, the fiscal authority running larger deficits whether spending more or purchasing other assets similarly. If the fiscal authority fears larger deficits or the monetary authority's willingness to absorb them, there is no reason they can't subsume some of the monetary authority's powers, suspend borrowing and merely credit their accounts with any amounts they deem necessary. We have no reason to fear deflation other than our own unwillingness to do what is necessary.
If one views the recession as one of supply, a resource one, specifically oil, the problem is real and the solution much more difficult. Oil is fairly unique in this regard. No other resource is as abundant in use and as difficult to substitute with substitutes generally being much more expensive. Its price seeps throughout the economy into everything. While inflation is low and unemployment is high, oil is still high at 2005 levels. Inflation could increase growth but even moderate growth could cause us to hit the supply wall and cause oil prices to increase faster than the economy can grow. They doubled over 2006-2008 and will do so again. The economy can adjust to moderate price increases, but prices can always increase by more than this. They must, since that is the only way for the market to balance demand and supply since supply is lagging. So unemployment may be the cost of keeping demand in check. Now inflation is low and somewhat higher inflation could be tolerated, but it could also shorten the time until we next hit that supply wall. The solution in this case is to accelerate development of alternatives though it is difficult to accelerate what is already urgent.
Let me say that I do not believe oil caused this recession. I do believe it could cause one though. I believe it lowered the growth rate to near zero and that we are growing now because it has fallen and if we grow much faster it will double again causing growth to collapse again and that we won't be able to grow solidly again without oil collapsing or competitive alternatives.
So does one increase inflation and growth now at the risk of a recession sooner or try to buy time for alternatives and supply to increase before one hits at the risk of incurring one now? It a balancing act.