Lets say I provide you with $100 000 with the only caveat that it has to be spent. The money is counterfiet, but perfect and would never be detected. You spend that money, increasing the demand for goods and services, and in such a short time production capacity can not be increased, causing a spike in inflation. So while other people have decrease spending you are increasing yours ( and those that you purchase goods from can also increase their spending as well. The $100 000 even though it increased inflation has kept demand for goods and services higher keeping people employed. It would of course run its course once the initial $100 000 has been spent.
The US is engaging in a period of deleveraging (except for federal government) deleveraging means that money is being taken out of the economic system. Reducing demand for goods and services, this is outside of any effects of inflation or deflation (although it is deflationary normally). Now if all sectors are engaging in deleveraging, the reduction in demand is extremely drastic. Overall imagine if 10% of all economic activity in the US ended tommorow, how many people would be laid off, what would happen to asset prices etc.
In the economic environment the US is in right now, government sourced demand is maintaining economic activity in the US. Keeping employment above the rate in which it would be otherwise.
So while inflation is costing jobs, the number of jobs it is costing in todays economic environment is lower then what would occur if the government (and fed) was not encouraging inflation through QE and additioinal government debt. The issue is that by taking the stance that they are, they are improving economic conditions today at the expense of economic conditions in the future. The economy in the future will not be as strong as it would be, but todays economy is stronger then it should be