The main way in which the New Deal was not successful was in the fact that it did not end the Great Depression. Instead, the Depression lasted until the US started to gear up for WWII. Even as late as 1940, the unemployment rate in the US was much higher than it had been before the start of the Depression. In addition, the gross domestic product (GDP) of the US was still lower in 1940 than it was in 1929. Those are the two most important measures of a country's economic strength and the New Deal failed to get either of them back to pre-Depression levels, even 7 years after the start of the New Deal.
Although the New Deal was a success in many ways, it failed to end the Depression. This is the main way in which it was not successful.
Whether or not the New Deal was a success depends on what you consider as the major goals of the policies. It could be viewed as a success in that the federal government’s role in the economy significantly improved, especially with the democratic way President Roosevelt handled his policies.
The New Deal contained programs for relief, recovery, and reform after the depression, setting forth various plans to solve unemployment and provide welfare. The policies did succeed in solving a few of the problems such as reducing unemployment as exemplified by the Civilian Conservation Corps, which provided work experiences for at least 3 million men under the age of 25.
However many of the created jobs were classified as “forced labor” that only gave temporary relief, which led to many economists suggesting that the New Deal ended up extending the Depression. The real recovery from the Depression did not occur until the 1940s, when war production gave the economy a boost.
So it really depends how you look at it- if the goal was to expand the power of the government in the economy, yes the New Deal was a success. But if the goal was to end unemployment and bring back economic prosperity, Roosevelt could have done better.