To cut it close is to barely manage a deadline. This expression can also be used to talk about working under a tight schedule.
Read the sample conversation given below.
I’ve got a pretty tight schedule today!
Varun: Hi Aryan, do you think we could have a talk sometime today?
Aryan: I wish we could, but I’ve got a pretty tight schedule today!
Varun: Oh, so what have you got going on?
Aryan: Well, I’ve to give a presentation at 10. That would keep me busy until 11.30. And then I’ve to drive home, pick up my son and drop him at school. After that, I’ve some important meetings over lunch. I guess I won’t get a break until 5 o’clock.
Varun: Wow, that’s cutting it close.