most precious bequests of the Founding Fathers.

Conservatives often drew upon the rhetoric of the Founding Fathers in opposing the New Deal, giving the impression that FDR's policy was somehow un-American, that it represented a radical departure from the traditions that had made America great.

At the same time, the New Deal also came under fire from liberals, who argued that though the policy was fine as far as it went, it wasn't sufficiently ambitious in scope or execution to deal with the pressing problems of the hour.

Liberal critics of the New Deal felt that it provided, at best, only the amelioration of existing economic conditions rather than dealing with the structural problems in the American economy that had given rise to such conditions in the first place.

For instance, many liberals argued that the government should create more jobs under the New Deal to counteract the many structural problems in the job market laid bare by the Great Depression. The free market, they maintained, could not be relied upon to create jobs by itself; a bigger role was therefore needed for government.

Liberal critics of the New Deal were, to a considerable extent, vindicated by the fact that it was only America's entry into World War II in 1941 that the scourge of mass unemployment was finally ended.

Both conservatives and liberals criticized the New Deal. Conservatives believed the government was doing too much. Conservatives supported a laissez-faire government policy toward the economy. They viewed the New Deal programs as giving the government too much control. They felt the Securities Act and the Glass-Steagall Act gave the government too much control and regulation of the stock market and banking industry. They felt the government spent too much money on job creation programs. The Civilian Conservation Corps, Civil Works Administration, and the Public Works Administration were examples of programs that cost a lot of money. The conservatives didn’t like that the Wagner Act gave unions the right to exist. They also believed the National Industrial Recovery Act established too close of a relationship between workers, businesses, and the government. Conservatives were also concerned about the growing debt of our country.

Liberals felt President Roosevelt didn’t do enough. They wanted to see more programs to help the needy and to create jobs. This led to the passage of the Works Progress Administration. They believed there should be a pension for the elderly. This led to the development of the Social Security Program. They wanted workers’ rights to be protected. This, along with the National Industrial Recovery Act being declared unconstitutional, led to the passage of the Wagner Act. President Roosevelt was concerned he might lose support from the liberals in the election of 1936. This could have hurt his chances of getting reelected.

President Roosevelt was criticized by liberals for not doing enough and by conservatives for doing too much.

It is interesting to examine certain programs started under the New Deal and realize that some of the feelings that the politicos of the time had about them have been realized.

One program about which conservatives were skeptical is the Social Security system which began in 1935 with the Economic Security Act of 1935. Taxes for this act were begun in 1937, and until 1983 it was a pay-as-you-go program.

The 2014 Social Security Trustees report showed a continuation of the current trend toward insolvency of both of its trust funds. As in the previous two years, the Trustees estimate that Social Security's combined retirement and disability trust funds will become exhausted in 2033, less than 20 years from now.

Another program that conservatives disapproved of was the Tennessee Valley Authority which they felt was socialistic in design. The TVA certainly has been a successful venture and has provided electrical power to many places that hitherto had had none. Moreover, it controls the Tennessee River flood waters and has improved navigation. So, in hindsight this was a program that produced jobs for many and has proved profitable. Still conservatives may have pointed to it as the beginning of government control over what should be left to private enterprise. 

Progressives were glad that FDR pledged to re-create the war social programs of the Wilson administration, a goal that was wildly popular at the time.

“I want to assure you,” Roosevelt's aide Harry Hopkins told an audience of New Deal activists in New York, “that we are not afraid of exploring anything within the law, and we have a lawyer who will declare anything you want to do legal.”

Some of them even called for FDR to become a benevolent "dictator," and do even more.

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Additional Source:  http://www.marketwatch.com/story/social-security-is-in-crisis-2014-07-31

Of course, liberals and conservatives had different reasons for criticizing the New Deal.

To conservatives, the New Deal was socialism.  It used taxpayer money to help people who were in need.  That is redistribution of income and it can be seen as a step towards socialism.  Conservatives saw it in this way.

To liberals, the New Deal did not do enough.   Many liberals wanted to see much more in the way of government spending.  For example, Dr. Francis Townsend wanted the government to give very generous pensions to all seniors on the condition that they spend all of their stipend every month, thus increasing demand in the economy.  Liberals, then, wanted more radical action than President Roosevelt was willing to take.

First, it should be noted that the New Deal was wildly popular—Roosevelt won reelection in 1936 in a huge landslide.

That being said, as the other answers have noted, Roosevelt was caught in the crossfire of being too radical for some and too conservative for others. The right was alarmed, as they still are today, at the idea of large government interventions into the economy. They felt that government jobs, Social Security, and other government programs robbed people of initiative, and that legislation for a forty-hour work week, the end to child labor, and minimum wage laws interfered with free markets.

On the left, Roosevelt was criticized for compromising too much with the private sector and not nationalizing basic industries. He also failed to implement a government health program, and while government programs employed many people, many still remained unemployed. Critics on the left wanted the kind of massive government spending that did not come until World War II—which then lifted the country out of the Depression. They thought Roosevelt was doing too little and allowing the country to merely limp along.

The left also criticized Roosevelt for not doing more to address civil rights and black equality. Roosevelt felt he could not risk losing the support of the South and so would not rock that boat. He felt that, inevitably, improving the social safety net with programs and policies such as minimum wage and Social Security would help black people to prosper as well as disadvantaged white people.

Critics on both the left and right labeled the New Deal fascist. On the left, critics condemned the control of the New Deal by big business interests and thought it stood for capitalistic ideals. However, on the right, critics took exception to the New Deal’s control of business and economy. They believed the government’s involvement in the economy as per the New Deal’s propositions was too much. The American Liberty League for instance, termed the New Deal agenda dictatorial. Also, critics on the right such as the conservatives argued that the New Deal was a “socialist” reform that would interfere with the economic wellbeing of the country as the government was focused on activist programs. On the left, liberals and radicals criticized the New Deal for not providing enough relief and failing to redistribute political and economic power to marginalized groups.