Green’s Dictionary of Slang

to pressurize, to intimidate.

1931		Irwin Amer. Tramp and Und. Sl. 99: High Pressure.-To force or argue another into a deal or action; to intimidate.
1940		W.R. Burnett High Sierra in Four Novels (1984) 363: Stop trying to high-pressure me. It’s no use.
1967		(con. 1920s) J. Thompson South of Heaven (1994) 27: ‘The high pressure?’ ‘The bosses [...] like the bosses are always high-pressuring the working stiffs.’.