Yes, not very often but sometimes if you are given a short amount of time to achieve something you can use it. I live in England though, and I think we use more phrases and expressions than they do in America.

I use this expression. If I travelled to work and arrived a few minutes before I am required to start, I would be "cutting it close", because I would almost be late. Other expressions that are similar would be, "that was a close call" or "that was a near miss". Often these expressions are used when talking about sports or situations that might be dangerous. Hope this helps