Green’s Dictionary of Slang

City Hall n.

In phrases

you can’t fight City Hall (also go fight City Hall)

(US) you can’t win against the establishment.

1941		A. Kober My Dear Bella 63: Mr. Gross looked at his wife and shrugged his shoulders in a gesture of helplessness. ‘Nu go fight City Hall!’.
1949		E. Rosenberg [bk title] Go Fight City Hall.
1961		L. Schecter Roger Maris 116: Maris was trying to play it cool. ‘What’re you going to do,’ he said at first, ‘fight City Hall?’.
1973		Chopper Mag. Jan. 60/2: You can’t fight the man, City Hall, and Johnny Joe Citizen.