In a story I am reading I came across the line:
「心までは砕けていないので、今は勘弁してください」
The context is that a waitress gets injured and a waiter (the main character) discovers this, gives her some ice, then answers the call of a customer who is in need. This line is what he says to the customer after she says (essentially) "What happened to the waitress?". The customer is surprised that not her original waitress, but a different person (a waiter) came for her.
Literally, this seems to mean "(her) heart is not broken, so please give (her) a break now". However, this doesn't seem to fit the context at all. Maybe the subject is actually the main character?
You can see the context here if necessary. The line is about 2/3rds of the way down.
Maybe the expression is being used in some ironic/sarcastic sense?