I second the accelerator pump as a possible issue. I cleaned my Rochester type B carburetor three times before I found the tiny port that the accelerator pump discharges into the carb throat was partially blocked. Assuming it’s a Rochester type “B” this may help.
Rochester Carburetor Information, Installation and Service Bulletins - Pre 1960Thanks to
Keith Hardy’s Old Online Chevy Manuals, for providing us this wealth of information.