In short, its not at all clear that nominal targeting will work as promised—much less generate real economic growth. And it could set off a deflationary spiral that would lead up into low growth and rising prices. In other words, stagflation.
A deflationary spiral that leads to rising prices? What a contradiction!
But stagflation is a possibility. The problem won't be a deflationary spiral. It is rather that if the productive capacity of the economy has been greatly depressed, and the current level of real output is approximately equal to productive capacity, then a shift to a higher growth path for nominal GDP will generate higher inflation. Real GDP will remain at its current low level (relative to the trend of the Great Moderation.) Presumably employment would remain low and unemployment would remain high. Inflation would be high for a time, before settling back to a slower trend rate once nominal GDP reaches the target growth path. High unemployment and temporarily high inflation--stagflation.
However, the problem wouldn't too much debt or odd arguments where people accumulate money that is losing value. The problem won't be that increased demand reduces demand and creates inflation.
The problem would be that firms cannot expand production because they will face bottlenecks. Perhaps there are key employees they cannot find, or special machinery, or some other kind of resource. And so, if the impact of nominal GDP targeting is simply more inflation and little or no real growth or employment, what would be observed is shortages of output as firms struggle unsuccessfully to meet rising sales.
It is important to understand that the problem wouldn't be excessive debt. The problem would be that the productive capacity of the economy fell in about 2007. Nominal GDP targeting keeps the flow of spending on output steady in the face of shifts in the productive capacity of the economy. The result is a higher price level and temporarily higher inflation. Advocates of nominal GDP targeting believe that this is the least bad environment to make the needed adjustments to such a decrease in productive capacity.