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A large part of the New Deal was makework programs to give some of the nearly 13 million unemployed (over 20% of the labor force) something somewhat productive to do. The WPA, the CCC, and the NYA were all programs of that ilk.
With the war on, that problem essentially went away. Pretty much every able-bodied male was expected to either join the military, or be helping with the new war production needs. In fact, they got so hard up for labor that a lot of women entered the work force who wouldn't have otherwise been there.
So the problems that those programs were invented to solve went away, and thus there was no need for the programs anymore.
Here's the issue in visual terms. Note that the war itself started in 1939. The USA joined right at the end of 1941, but was producing arms for the Allied side much earlier.
The CCC was shut down in 1942, NYA and WPA in 1943. You can see from the graph that its was pretty clear by that time that they were no longer needed. So it wasn't the war directly that caused their demise, but it probably indirectly did.
Upvote:2
During the Great Depression, arguably the most important problem was unemployment, which at its peak reached nearly 25% of the work force, or 11 million people.
The start of World War II, solved that problem. By 1944-45, the U.S. armed forces reached 11-12 million in strength, roughly matching the maximum number of unemployed cited in the previous paragraph. That's not counting the people that were employed in military related industries. By 1945, there was an issue of overemployment, with people working multiple shifts, and women entering the work force.
The programs that you referred to that were cancelled mostly addressed the employment problem, because they were "make work." And yes, the money that was formerly directed to these programs went to fund the war effort (and the "reemployment" of these people).
Other parts of the New Deal, such as the banking legislation and the Tennessee Valley Authority remained in place.