。
I don't want to draw the short straw.
Literal
Unlucky-lot [object-を] don't-want-to-draw.
貧乏くじを引く is a set expression meaning 'to draw the short straw' or 'to end up with the worst deal.' 貧乏くじ literally means 'poverty lottery ticket.' The negative desiderative ~たくない expresses the speaker's desire to avoid this outcome.