It’s more like the “Red Guards” than the Brownshirts.
Obama is using both. The Brown Shirts are the Kristallnacht rioters who smash glass, burn cars and stop traffic on the streets. The Red Guard are the student bodies who scream at conservatives who attempt to speak. The Red Guard destroy the university tradition of open campus, rational discussion of all ideas.
The Brown Shirts are on the street looking for trouble. They will fight, burn, and destroy at will.
Both groups are predominantly children in their teens who are incapable of discernment and easily led into idealistic, utopian ideology.