In addition to what Steve Benen says on the subject of the New Deal, it’s important to distinguish between the structural reforms (i.e., “New Deal”) that FDR implemented during his time in office and FDR’s efforts to bring about an economic recovery.
The first Social Security check didn’t go out until 1940. Under the circumstances, it obviously wasn’t a very effective Depression-fighting initiative for a President inaugurated in 1933. But that wasn’t the point — it was just a good idea that would have been a good idea to implement in the 1920s or 1890s or whenever, but it took until the 1930s to create a political situations in which it could be enacted. Social Security does act as something of an economic stabilizer in preventing or mitigating recessions now that it’s in existence, but clearly it didn’t do much of anything to ameliorate the Depression of the 1930s.
So when people talk about a new New Deal, it’s useful to separate two different ideas. One is to say that we should respond to the current downturn with large-scale fiscal stimulus. The other is to say that we should take advantage of downturn-born progressive majorities in congress to pass a lot of worthy structural reforms. These both sound like good ideas to me, but they’re separate ideas and one could accept one and reject the other.