One of the major attractions of communism to some is the idea that it could solve the problems caused by capitalism. One of the major problems connected to capitalism is the fact that capitalism can lead to poverty for some. During the 1930s, this problem was extremely severe. For that reason, some Americans were attracted to the Communist Party.
The 1930s, of course, was the decade of the Great Depression. During this time, it seemed to many as if capitalism had failed. It appeared that capitalism had caused the mass of Americans to become poor. This made many people think that an alternative would be preferable to capitalism. Since communism was the major alternative available, many people became attracted to that ideology.
Overall, then, the reason that some were attracted to communism during this time was that it was an alternative to the capitalist system which appeared to have failed.