Roosevelt was called a socialist loudly, frequently, and from all directions.
It started when he was governor, before he even started his first campaign for president. During that 1932 campaign, even President Herbert Hoover got into the action, saying the New Deal would mean "the total abandonment of every principle upon which this government and the American system is founded."
After Roosevelt was sworn into office, the attacks intensified. "The productive industries of the United States are faced today by the gravest danger that has ever confronted this country during the whole period of its growth as an industrial nation," declared Virgil Jordan, president of the National Industrial Conference Board, who said the United States was being carried to a stage of "outright socialism."
One of the favorite speeches I came across while researching your question was one from Sen. Henry Hatfield, a Republican from West Virginia. On May 30, 1933, he compared Roosevelt and the New Deal to Stalin, Mussolini and Hitler -- in the same speech. "The 'New Deal,' while it sings the praises of Jefferson and Jackson, is more in keeping with the preachings of Norman Thomas, Stalin, Mussolini and Hitler. Since March 4 we have had proposed by the chief executive, and the Congress has enacted, more out-and-out socialistic legislation than has ever been enacted in a similar period by any major power other than Soviet Russia.
Of course, there were people saying the opposite, too. Norman Thomas, whom Hatfield mentioned above, was the Socialist Party's candidate for President in 1932 and ran against Roosevelt. In a New York Times column in June 1933, he said of the New Deal: "... in all this, he has not ended, but has rather strengthened, the basic principle of capitalism, which is not and has not been for a long time economic individualism, but the right of private ownership of productive goods and their operation for private profit."
In short, the New Deal wasn't socialist, but it did lay the foundations for state capitalism.
In conclusion, I want to leave you with an outside perspective. For a time in 1933 and 1934, there was a fad of foreign writers coming to the United States to write about this resurgent America shaking off an economic depression under a vibrant, charismatic new president. Take a look at this column by Andre Maurois, a French novelist and essayist, and imagine it being written not in 1933, but 75 years later ...