why does deficit spending lead to inflation
The bonds issued by the government to finance the additional deficit-spending will lead to more inflation because they will be purchased by the central bank or private banks with newly-created money. As noted above, an increase in government spending cannot possibly help. Its likely effect will be to PROLONG the downturn, but the longer it takes for a sustained recovery to begin the greater the opportunity for the government to 'fight' the downturn via even more inflation-financed spending.