No, it doesn't. It's often used as a joke. It means "Now you've gotten lucky, don't be greedy and try to get even more out of it." For example: If I steal an apple from the fruit market and, after eating it, I say to my friend "Now let's go and steal a hamburger!!", he might say to me "Don't push your luck." By the way, allow me to say, you have a beautiful foot and a beautiful cat.

We use this expression when somebody has crossed the lines of social acceptance or is annoying us or somebody else. We can also use it jokingly but it is less common and the meaning is different.