The group that most strongly opposed the New Deal was conservatives. They did so on ideological grounds. To true conservatives, the New Deal appeared to be a socialist program. To conservatives, it was clearly not the place of the government to intervene in the economy. Conservatives felt that programs like the AAA or NIRA or TVA constituted government planning of the economy instead of the free market system that conservatives prefer. Conservatives felt that government relief to unemployed people was redistribution of income meant to achieve the socialist vision of a society where everyone has equal wealth.
To be sure, there were critics of the New Deal on the left. Critics like Huey Long felt that the New Deal did not go far enough towards helping the poor. However, I would argue that it was conservatives who most strongly opposed the New Deal.