I get my braces of in 15 days but I broke a bracket 4 days ago. Will they push the day they come off back?

Yes, they might have to push back the day you get your braces off.  You should give your orthodontist a call and explain what happened (which bracket came off).  They may want to see you right away depending on which bracket came off.  Depending on the location of the bracket, and forces that are being placed on the teeth (such as Power Chain) a tooth can move very quickly and extend your treatment several months, or on the other hand there can be no movement and it is not a problem to leave the bracket off.