Parir (pah-REER) means to give birth. Chayote (chah-JAW-teh) is a type of squash from Mexico, with a soft, delicious flavor and a skin covered with thorns. Parir chayotes means to be in a painful situation that feels (figuratively, of course) as "giving birth to round squashes covered with thorns." It is informal but not offensive.
Ando pariendo chayotes en la chamba. ¡La fecha límite para entregar el reporte era hace dos semanas!
I'm in a tough spot at work. The report was due two weeks ago!
The image shows a chayote. Parir chayotes is quite a graphic allusion to hardship.