Obviously, conservative groups viewed the New Deal as a massive violation of property rights as well as an unwarranted intrusion into business. Business leaders objected in particular to Roosevelt's perceived favoritism toward unions, which was put into law by the Wagner Act. Conservative leaders were, however, never able to break Roosevelt's New Deal Coalition, and while their opposition shaped his policies, including the cuts in spending in 1937, they could not stop the thrust of his reform plans.
Other opposition came from the left, and included populists like Huey Long, Charles Coughlin (not exactly a leftist, but did propose radical wealth-redistribution plans) and Francis Townsend, whose plan for a $200 pension for all Americans over the age of 65 helped popularize the concept that would later become Social Security. Basically, these men and the millions who followed them argued that the New Deal had not done enough to achieve economic justice for working class Americans.
The Supreme Court opposed the New Deal because many of its proposed programs violated the Constitution. Once such violation was the Agricultural Adjustment Act, which seeked to tax food processors whose revenue would be given to farmers. The court correctly argued that it was illegal to tax one group in order to pay it to another. Roosevelt responded by "packing" the court, which was another Constitutional violation that remained unchecked.
The legacy of the New Deal was that it illegally expanded the power of the Executive Office.
Many people who feared the growth of government and worried about the intrusion of the federal government into the economy were skeptical of the New Deal. They argued that politicians might create programs that were financially unsustainable and that politicians might use federal funds to buy votes, leading eventually to massive deficits and huge unfunded liabilities. They worried that politicians might make promises that would commit the government to policies that eventually would bankrupt the country. They also argued that many of the programs would not work and would be wastes of money and would result in massive bureaucracies.
Conservatives were the strongest opponents because they saw this as a way of making America into a socialist country. Populists like Huey Long, however, argued that it was not extreme enough. Upton Sinclair, for example, pushed hard for more relief to the poor, running for governor of California on such a platform.