The answer to your question is dependent on what your definition of "working" is looking for. I'll provide a couple examples to keep it all encompassing. (Also i'm assuming you're wondering about Roosevelt's New Deal rather than the Canadian counterpart Bennett's New Deal)

The two major concepts leading the overarching New Deal ideology were the National Industrial Recovery Act (NIRA) and the Agricultural Adjustment Act (AAA). NIRA essentially allowed business leaders to create a set of codes for their workers allowing them to form unions, set production limits and set against unfair competitive practices. The AAA looked to lessen surplus farm production, which in turn lowered crop prices, by offering payments for the reduction.

NIRA didn't do so well, as it's basis that competition had ruined the economy was not the most correct idea. The individual business that took part in this system were administered by the NRA (National Recovery Administration). The NRA faced issues, as the majority of the businesses were of major corporations, not small businesses, which were those most hurt economically. So in this sense, the New Deal did not "work" per say. Although the aforementioned AAA resulted differently.

The subsidies offered by the AAA were enticing to farmers, resulting in the destruction of 8.5 million piglets and to plow under crops in fields. This effected millions of hungry Americans, so in the short term this did not really work out so well either from a social perspective. This also hurt sharecroppers (those who were in groupings that worked on another person's land for a share of the yield), who had to leave the farming land due to a cut of production. But the subsides did help the farmers economically.

With the move away from agriculture this left many Americans jobless, which Roosevelt combated the implementation of relief. Focusing primarily on work relief, versus monetary relief, this created many jobs in the industry and trade sector. Building roads, dams and other infrastructure.

The results of these New Deal policies were seen as effective. Within 3 months, employment fell from 13 million in 1933 to 9 million in 1936. Farm prices rose, along with wages and salaries.

Socially, the New Deal spurred the agency of Roosevelt's wife Eleanor Roosevelt. She looked to create her own place within the ideals of the New Deal aside from FDR, showing a new sense of Agency within the First Lady, before this unprecidented, as well as female agency as a whole. She traveled across the nation speaking about her views that the nation faced as well a political issues. She looked at sweat shops and child labour, as well as advocating her support for veterans and teachers. These issues and her advocacy, within her title as First Lady, showed that the introduction of the New Deal was substantial socially, and arguably spurred these questions on social change.

Finally as an aside, I think it would be beneficial to not look at history as a "correct belief" versus an incorrect one. Each source and the perspective it brings gives the historian a unique understanding of the world from a specific lens. The sources I offered focused on the beneficial components of the New Deal, but merely glanced on the social and cultural repercussions that the farmers and small business had when the systems of the new deal were in an experimental phase. This can suggest a multiplicity of other sources that detail these struggles. The short and dry of the economic results show that the New Deal was beneficial. Whether this perspective is correct depends on the historian/ reader and what they want to look for in a historical source.

A People & A Nation - Mary Beth Norton et al

Eleanor Roosevelt as First Lady - Allida M. Black