Green’s Dictionary of Slang

1. the last card; the final play or thing in any series.

1914		Jackson & Hellyer Vocab. Criminal Sl. 18: blow card [...] Current amongst gamblers and genteel grafters. Any use less thing or condition; financial embarrassment; the last card; the final play or thing in any series. Examples: ‘Don’t connect with this wop, he is on the blow card,’ i. e., broke. ‘Pull this one off and call it the blow card’.
1950		Goldin et al. DAUL 30/1: Blow-card. 1. A worthless playing card drawn in a game which ruins a potentially winning hand.

2. in fig. use.

1950

Goldin et al. DAUL 30/1: Blow-card. […] 2. Any thing or event that spoils what had appeared to be a promising situation. ‘The touch (theft) was a pushover till the rumble (interruption) came. That gapper (passerby) spotting us was the blow-card.’.