It is credited that WW2 stopped unemployment, but why did his new deal struggle to alleviate unemployment as compared to the effect of increased industrial output in WW2?
The New Deal seems a lot like fiscal expansion, because people focus on its public works programme and social security programme, but it really wasn't. It was in fact mostly structural and broadly budget balanced, financed by high tax rates, fiscal contractions like cutting government wages, and minimal debt, so net government spending never actually increased significantly, unlike during the war. Consequently, net government expenditure only increased by 4.8%, and output recovery was slow and spotty. That being said it had some successful monetary policy and though the war brought a massive wave of demand expansion, the New Deal definitely helped, with Christina Romer (2005) dating recovery to the New Deal.
The Keynesian argument that the Great Depression ought to be resolved by fiscal expansion was not embraced by Morgenthau, the Treasury Secretary, who was a strict monetarist. To his credit, Morgenthau's method of a sharp and sustained drop in interest rates would have been correct for most conventional scenarios, except the Great Depression was so serious the stabilising nominal interest rate level would have been negative, hitting the Zero Lower Bound. Today we have different types of unconventional monetary policy to deal with this, but back then Keynes proposed fiscal policy as a blunt force inflationary sledgehammer.
What was successful was the monetary policy of taking the dollar off the gold standard temporarily. This allowed the dollar to depreciate by about 20%, giving a much needed export boost. What was less good were price controls, aimed at forcing prices of agricultural products upwards to stimulate inflation expectations. Morgenthau opposed this, arguing that any kind of sustained inflation was necessarily a monetary phenomenon, but Roosevelt pushed through anyway. By 1934, inflation had barely moved but people began starving in the cities even as millions of unbought pigs were slaughtered.
The best way to see why this was insufficient is to consider what was sufficient. The country which handled the Great Depression the best was actually Japan, which would later become the playbook for future economic catastrophes. Under Takahashi Korekiyo, a three pronged proto-Keynesian policy consisting of fiscal expansion through government infrastructure and military projects, exchange rate policy through 60% devaluation, and monetary policy through a 50% rate cut, meant that the Great Depression in Japan only lasted from 1929-1930. By 1937, Japan's real industrial production index was double that of 1929.