I’m one of those people who when I need space to calm down and I clearly state this out loud in plain English, I need it promptly. It is no longer a request, but a basic expectation from my overwhelmed brain for the other party to back off and leave me alone. I can then return to the difficult discussion later, when I’m level-headed. That “later” may be in a short while or a long while, depending on the particular situation, topics(s) of concern, the other party’s own emotional state, etc. Once in a while, I have found this boundary I set to be difficult for some people to respect. Space, often not only the final, but very necessary, here-and-now frontier.
(I do so appreciate the bulk of people kindly allowing me space when I need it. And I am ever so glad to reciprocate this need for others.)