The landlord is going to "pinch" the tenant for not paying rent.
During the recession, lots of people cannot afford their rent, so they are being "pinched."
He is behind on his rent; therefore, he is facing "pinching."
According to some interpretations, the song "Pinch Me" by the "Barenaked Ladies" uses this term with this meaning. The narrarator is
unemployed and cannot pay his rent, and he is resigning himself to his
inevitable fate of homelessness.