Like Cole and Ohanian, I do not think that large expansions in the size and scope of government spending programs were desirable. While I can see various pathways by which additional government spending might increase demand overall, monetary institutions that keep nominal spending on output on a slow, steady growth path are a much better approach. It is in that context that the opportunity cost of government programs can be better perceived, and further, any benefits of government programs, particularly social spending programs, can be understood.
However, Cole and Ohanian want to argue for a "supply only" account of the Depression. I agree there is some growth path of prices and wages that will allow real expenditures to remain equal to the productive capacity of the economy, given almost any growth path of nominal expenditures. Cole and Ohanian, however, are mistaken when they claim that falling prices and wages were generating a recovery of real output near the trough of the Great Depression.
David Glasner's response shows that rising demand appears to have been causing both higher production and prices in the fall of 1932. Unfortunately, soon after, demand began falling again as did both output and prices. A sustained recovery in demand only began in March of 1933, with both output and prices rising after the suspension of gold payments.
Of course, Cole and Ohanian might respond that prices and wages needed to be lower still, and I would agree--leaving aside the possibility of reversing the massive decrease in nominal expenditure. However, I would like to emphasize that the Hoover and Roosevelt anti-supply-side policies aimed at keeping prices and wages from falling and trying to force them back up were not some kind of bolt from the blue. If money expenditures on output had continued on the growth path of the twenties, it is unlikely that Hoover would have decided that nominal wages should be suddenly hiked to generate even more rapid growth. And Roosevelt might never have been President, much less supported or passed an unconstitutional grandiose scheme of price fixing. How successful would have labor organizers been if they didn't have the argument that the bosses are trying to cut your wages? How much political support would pro-union legislation have had if there had not been surpluses of labor and both the incentive and ability to force pay cuts?
Allowing money expenditure on output to fluctuate while depending on widespread wage and price adjustments to keep real expenditures equal to productive capacity seem to be highly counterproductive. To me, both the Greater and the Lesser Depressions are showing that to be true.