Why do you think people supported new deal critics such as huey long and father coughlin?

Poor people who wanted economic equality supported New Deal critics like Long and Coughlin because their proposals called for redistribution of wealth.

Huey Long was a strong populist who served as governor of Louisiana from 1928 to 1932, and then Senator representing Louisiana from 1932 till 1935 (when he was assassinated).  He spoke out against bankers and wealthy elites.  Thinking President Roosevelt's New Deal didn't go far enough, Long introduced his own idea:  "Share Our Wealth," a program that would tax people on their net assets and redistribute that wealth to the needy.

Father Charles Coughlin also accused Roosevelt of being too cozy with the bankers.  He preached a message of social justice and established the National Union for Social Justice.  Coughlin's message aired his thoughts on a radio program -- and some of those thoughts were anti-Semitic, aimed against the Jewish community (and particularly Jewish bankers).  His radio program was cancelled in 1939 because of such controversial content.

The new deal citics drew support from some quotas because of their spirited arguments about how new deal policies would affect big companies, and multinationals that are the life line of American labour force.

Roosevelt policies  found critics from quarters such as conservative democrats,and republicans.