The phrase putting out fires means dealing with many small problems, usually at work. Though the problems might be small, they need to be solved quickly before they become bigger ones.
Sorry I didn’t have time to meet you for lunch today. I was busy at work all day putting out fires.
Sometimes it feels like you get nothing done in the office – you need to spend the whole day putting out fires.
To get on like a house on fire. If you say two people get on like a house on fire, it means they like each other and find it very easy to become friends – they get on very well together.
Phoebe and Alice get on like a house on fire. They share exactly the same sense of humour and are always joking and laughing together.