This is an idiom to appeal to those kinaesthetic readers who like to feel and do. It basically refers to the moment when a situation becomes serious, after the play or the circling around the topic, one party decides to take action. This action could be tough or hard and received as aggressive or it could simply mean that things are becoming serious and you need to respond. It corresponds to the first part of “When the going gets tough…”
Sometimes used as “If push comes to shove”. A shove is a more aggressive push and is usually used metaphorically here.
There are many theories related to the origin of the expression including references to rugby and giving birth with none seeming definitive.
If push comes to shove, she won’t kick her daughter out of the house.
He always backs down, when push comes to shove. You can’t rely on him to do what he promises.